JP2001092789A - Calculating device and storage medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a calculating device which is used for a scientific electronic calculator having graphic display function and capable of facilitating specification of a closed section to be surrounded by graphs of plural functional formulas and input operation of its range of integration to provide more effective integration arithmetic function in learning, performing display to enable prompt confirmation of the are of the closed section and integration formulas, etc., and clearly displaying the processes of special integration and a storage medium. SOLUTION: When the graphs regarding the plural functional formulas are displayed and a tracing instruction of the closed section is further inputted, cross point coordinates and apex coordinates of each graph are detected, values of an (l) register, an (m) register and an (n) register are set by updating them and an area to be surrounded by points to be specified by the values of each register is painted out and displayed as the specified closed section by a CPU 2.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a calculation device and a storage medium for performing an integral operation and a display control of a closed section surrounded by a graph of a plurality of functional expressions.

[0002]

2. Description of the Related Art Conventionally, a graph scientific calculator having a graph creation and display function has been used for educational sites and for technical calculations of engineers. The graph scientific calculator has various built-in function calculation programs, and can perform graph creation display based on an input function expression and integral calculation.

[0003] For example, the integral operation function of the above-mentioned graph function calculator detects a closed section surrounded by a graph of two functional expressions, executes an integral operation on the closed section, calculates an area value, and displays the area value. There is something that does
-12146). In this way, the graph scientific calculator can easily perform visual recognition by graph and mathematical recognition such as area value at the same time in a closed section, and its use range has been greatly expanded in recent years. Opportunities to increase.

[0004]

However, in the learning of integration in an actual educational site, for example, when there are a plurality of closed sections surrounded by a plurality of graphs, an area value and an integral equation for each closed section are obtained. Although it is necessary, in the conventional graph scientific calculator, a complicated operation such as a user inputting a mathematical expression indicating an integration range was required to specify which closed section to perform the calculation.

[0005] In the learning of the integral, a method for facilitating the integral is learned through a special process such as replacement integral or movement of the integral range. In a conventional graph scientific calculator,
There is no indication of the process of such a special integration operation, and it is not sufficient for use in learning.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a scientific calculator having a graph display function in order to provide an integral operation function more effective in learning. (1) Designation of a closed section surrounded by a graph of a plurality of functional expressions and its To facilitate the input operation of the integration range, (2) to display such that the area of the closed section and the integration formula can be quickly checked, and (3) to clearly display the special integration process. And a storage device for realizing the above.

[0007]

The present invention has the following features in order to achieve the above object. In the following description of the means, a configuration corresponding to the embodiment will be exemplified by parentheses as an example. Reference numerals and the like are reference numerals and the like in the drawings described later.

According to the first aspect of the present invention, there is provided a graph display means for displaying a graph of a plurality of function formulas (for example, C shown in FIG. 1).
PU2, display unit 6; S103 in FIG. 3; FIG.
Designating means (for example, the input unit 3 shown in FIG. 1; S104 in FIG. 3) for designating any one of the closed sections surrounded by the graphs of the plurality of function formulas, and the closed section is designated by the designating means. Display control means (for example, CPU2 shown in FIG. 1; S105 to S120 in FIG. 3; FIG. 4B) for changing and displaying the display format of the designated closed section every time
To (E)).

According to the calculation device of the first aspect of the present invention, the graph display means displays a plurality of function formula graphs, and any one of the closed sections surrounded by the plurality of function formula graphs is displayed. Is designated by the designation means, each time the designation is made, the display control means changes the display format of the designated closed section to be displayed.

Therefore, the desired closed interval on the graph is
Even if you do not have to input mathematical formulas for the integration range, you can quickly specify them with simple operations.The specified closed section is displayed in solid color, so you can easily check it visually. It is effective for learning of and integration.

According to a second aspect of the present invention, in the computing device according to the first aspect, the designation unit manually writes the closed section within the closed section on the graph displayed on the graph display unit. A paint designating means (for example, tablet 4 shown in FIG. 1; S in FIG. 5)
204; FIG. 6 (B)), and a designation deciding means (for example, as shown in FIG. 1) for deciding the designation of the closed section when the range painted by the filling designation means is a predetermined ratio or more of the closed section. CPU2; S205 to S2 in FIG.
06; FIG. 6 (C)).

According to the calculation device of the second aspect of the present invention, when the inside of the closed section is painted and designated by handwriting on the graph displayed on the graph display means by the painting designation means, When the filled area is equal to or more than a predetermined ratio of the closed section, the designation of the closed section is determined.

Therefore, the closed section can be designated by handwriting on the graph display, so that the operation of designating the closed section becomes easier. Further, since it is not necessary to strictly paint all of the inside of the closed section, the painting work can be simplified and the range can be quickly specified.

According to a third aspect of the present invention, in the computing device according to the first aspect of the present invention, an area value calculating means for calculating an area value of the closed section specified by the specifying means (for example, FIG. CPU2 shown; S111 in FIG. 3)
And area value display means for displaying the area value calculated by the area value calculation means (for example, CPU2 shown in FIG. 1;
It is effective to further provide (B) to (E) of FIG.

According to the third aspect of the present invention, when the closed section is specified by the specifying means, the area value of the closed section specified by the area calculating means is calculated, and the area value is displayed. Display by means.

Therefore, the area value of a closed section specified by a simple specifying operation can be quickly confirmed together with the display of the closed section, which is effective for learning graphs and area integration.

According to a fourth aspect of the present invention, in the computer device according to the third aspect, the display control means determines that a plurality of closed sections are designated by a plurality of designation operations by the designation means. Changes the display format of the newly designated closed section while maintaining the display format of the previously designated closed section, and displays the area value calculating means. It is effective to add the area value of the newly designated closed section to the area value and calculate the sum of the area values of the plurality of designated closed sections (S309 to S310 in FIG. 7).

According to the calculation device of the present invention, when a plurality of closed sections are specified by a plurality of specifying operations by the specifying means, the display control means specifies a previously specified closed section. The display format of the newly specified closed section is changed and displayed while the display format of the closed section is maintained, and the area value of the newly specified closed section is added to the area value of the previously specified closed section by the area value calculating means. The area values of the sections are added to calculate the sum of the area values of the plurality of designated closed sections.

Therefore, each time a designation operation is performed, another closed section can be designated while maintaining the designation of the previously designated closed section, so that a plurality of closed sections can be easily designated. . In addition, since the sum of the area values for a plurality of closed sections is displayed, analysis of various combinations of closed sections can be easily performed, which is effective in learning.

According to a fifth aspect of the present invention, in the computing device according to the first aspect of the present invention, an integral expression calculating means for obtaining an integral expression for calculating an area value of the closed section specified by the specifying means. (For example, the CPU shown in FIG. 1
2; S509 in FIG. 11); and integral expression display means (for example, CPU 2 shown in FIG. 1; S510 in FIG. 11; FIG. 12)
(D)) is effective.

According to a fifth aspect of the present invention, when a closed section is specified by the specifying means, the integral equation calculating means calculates the area value of the specified closed section. Is obtained, and the obtained integral expression is displayed by the integral expression display means.

Therefore, the integral expression for obtaining the area value for the closed section specified by the simple specifying operation can be quickly confirmed together with the display of the closed section, which is effective for learning the graph and the integral.

According to a sixth aspect of the present invention, in the calculation device according to the fifth aspect, when the specified closed section has a plurality of integration ranges, each of the integral formula calculating means includes a corresponding one. A range-by-range integration formula calculating means (for example, CPU2 shown in FIG. 1; FIG. 1)
1 (S506 to S518), wherein the integral expression display means displays the integral expression by range calculated by the integral expression calculation means by range (FIG. 12 (D)), and the display control means The display format of the closed section is further changed to a different display format for each of the integration ranges and displayed (S406 to S406 in FIG. 9).
S414; FIGS. 10C and 12C are effective.

According to the calculation device of the present invention, when the specified closed section has a plurality of integral ranges, the integral formula for each range is calculated by the integral formula calculating means for each range. Is calculated by the integral expression display means.
The calculated integral expression for each range is displayed, and the display format of the closed section is further changed to a different display format for each of the integral ranges by the display control means and displayed.

Therefore, the integral range within the closed interval can be easily confirmed on the graph display of the computing device, and each integral expression for each integral range can be confirmed. Is effective in learning integral.

According to a seventh aspect of the present invention, in the calculation apparatus of the first aspect, a replacement formula input means for inputting a replacement formula for replacing a variable included in the function formula with another variable. (For example, the input unit 3 shown in FIG. 1; S608 to S610 in FIG. 13; FIG. 14E) and the variables included in the function formula are replaced based on the replacement formula input by the replacement formula input means. The post-replacement function expression calculating means (for example, CPU 2 shown in FIG. 1; S612 in FIG. 13) for obtaining the post-replacement function expression and the graph of the post-replacement function expression obtained by the post-replacement function expression calculation means are displayed. After replacement graph display means (for example, C shown in FIG. 1)
PU2; S613 in FIG. 13; FIG. 14 (F)) and the graph displayed on the post-replacement graph display means.
A display control unit after replacement (for example, CPU2 shown in FIG. 1; S614 in FIG. 13) for changing the display format of the integration range after replacement corresponding to the closed section specified by the specifying unit.
To S618; E6 in FIG. 14 (F), a post-replacement integral expression calculating means (for example, CPU2 shown in FIG. 1) for calculating the post-replacement integral expression for the specified closed section, It is effective to further include a post-replacement integral expression display means (for example, CPU2 shown in FIG. 1; S619 in FIG. 13; FIG. 14 (G)) for displaying the post-replacement integral expression calculated by the integral expression calculation means. is there.

According to the calculation apparatus of the present invention, when a replacement formula for replacing a variable included in the function formula with another variable is input by the replacement formula input means, the function after replacement is input. The replacement function is obtained by replacing the variables included in the function formula based on the input replacement formula by the formula calculation unit, and the replacement function display unit displays a graph of the replacement function formula by the replacement graph display unit. By the post-replacement display control means, in the graph displayed on the post-replacement graph display means, the display format of the post-replacement integral range corresponding to the specified closed interval is changed, and the post-replacement integral expression calculating means And calculating the post-replacement integral expression for the designated closed section, and displaying the post-replacement integral expression by the post-replacement integral expression display means.

Therefore, it is possible to easily confirm the graph of the function formula after the replacement, the integration formula after the replacement, and the integration range after the replacement by the replacement mathematical expression. It can be clearly confirmed step by step.

[0029] As in the invention according to claim 8, in the computing device according to claim 1, when the closed section is designated by the designating means, the display control means sets the designated closed section. A display erasing means for erasing a graph display excluding a part constituting a section (for example, a CP shown in FIG. 1)
U2; it is effective to further include S705 to S712 in FIG. 15; FIG.

According to the calculation device of the present invention, when the closed section is designated by the designating means, the graphic display excluding a portion constituting the designated closed section is displayed by the display erasing means. Since the deletion is performed, the specified closed section can be displayed in an easily viewable manner.

Further, as in the ninth aspect of the present invention, in the calculation apparatus of the eighth aspect, the movement display control means (for example, the CPU 2 shown in FIG. 1) for displaying the designated closed section in parallel. S810 to S81 in FIG.
1; FIG. 18 (E)) and a moving amount detecting means (for example, CPU 2 shown in FIG. 1; FIG. 17) for detecting the moving amount in the closed section.
S813), and after-movement integral expression calculating means (for example, C shown in FIG. 1) for calculating an integral expression for the closed section after the movement according to the moving amount detected by the moving amount detecting means.
PU2; S814 to S817 in FIG. 17) and post-movement integral expression display means (for example, CP shown in FIG. 1) for displaying the post-movement integral equation calculated by the post-movement integral equation calculation means.
U2; S818 in FIG. 17; FIG. 18 (F)).

According to the calculation device of the ninth aspect of the present invention, when the designated closed section is translated and displayed by the movement display control means, the movement amount of the closed section is determined by the movement amount detection means. Is calculated by the post-movement integral formula calculating means, and the integral formula for the closed section after the move is calculated according to the detected moving amount. indicate.

Therefore, it is possible to easily confirm the graph display after the parallel movement and the calculation of the area after the parallel movement of the parallel movement of the closed section which is frequently performed in the learning of the integral. It can also be used when doing so, and the range of use of the computing device can be expanded.

Further, as in the tenth aspect of the present invention, in the calculation apparatus according to the first aspect, a graph enlarged display means (for example, a graph enlarged display means for enlarging a closed section designated by the designation means and displaying the closed section within a display range) CPU2 shown in FIG. 1;
(S905 and S912 in FIG. 19; FIG. 20 (C)) and when the closed section is enlarged and displayed by the graph enlarged display means, the coordinate value of the integral range of the closed section and the display position are eliminated so as to eliminate inconsistency. Correction means for correcting the display range (for example, CPU2 shown in FIG. 1; S906 to S91 in FIG. 19)
It is effective to further provide 1).

According to the calculation apparatus of the tenth aspect, when the designated closed section is enlarged and displayed within the display range by the graph enlargement display means, the correction section sets the closed section. The display range is corrected so as to eliminate inconsistency between the coordinate value of the integration range and the display position.

Therefore, it is possible to eliminate the mismatch between the coordinate values in the integral range of the closed section and the graph display position, and to perform more accurate graph display and integral calculation.

According to an eleventh aspect of the present invention, there is provided a graph display means for displaying a graph of a plurality of function formulas (for example, CPU 2, display unit 6 shown in FIG. 1; S1003 in FIG. 21; FIG. 22).
(A)) and a number calculating means (for example, CPU2; S1 shown in FIG. 1) for obtaining a number indicating a magnitude relationship of a predetermined amount for each closed section surrounded by the plurality of function formula graphs.
004 to S1010) and number display means (for example, CPU2 shown in FIG. 1; S101 in FIG. 21) for displaying the numbers obtained by the number calculation means by attaching the numbers to the respective closed sections and displaying the numbers.
1 to S1012; FIG. 22 (C)).

According to the calculation apparatus of the present invention, the graph display means displays a plurality of function formula graphs, and the number calculation means calculates a predetermined amount for each closed section surrounded by the graph. Is obtained by a number display means, and the number obtained by the number calculation means is attached to each closed section and displayed.

Therefore, for a plurality of closed sections, it is possible to easily analyze the order of the size of the area and the magnitude relationship of a predetermined amount such as the size of the x-coordinate value. In the learning, the relationship between the graph and a predetermined amount such as the area can be easily confirmed.

The invention according to claim 12 provides a graph display means for displaying a graph of a plurality of function formulas (for example, CPU 2, display unit 6 shown in FIG. 1; S1103 in FIG. 23; FIG. 24).
(A)) and a shape pattern creating means (eg, CPU2 shown in FIG. 1; S110 in FIG. 23) for creating a shape pattern of each closed section surrounded by the graphs of the plurality of functional expressions.
7) and an area value calculating means (for example, CPU2 shown in FIG. 1; S110 in FIG. 23) for calculating an area value of each closed section.
6) and a table creating means for creating a table in which a shape pattern created by the shape pattern creating means and an area value calculated by the area value calculating means are associated with each other for each closed section (for example, FIG. C shown in 1
PU2) and table display means for displaying the table created by the table creation means (for example, CPU2 shown in FIG. 1; S1108 in FIG. 23; FIG. 24B)
And, it is characterized by having.

According to the calculation device of the twelfth aspect of the present invention, the graph display means displays a plurality of function expression graphs, and the shape pattern creation means displays the shape pattern of each closed section surrounded by the graph. When the area value of each of the closed sections is calculated by the area value calculating unit, the table creating unit creates a table in which the shape pattern and the area value are associated with each of the closed sections. Is displayed by the table display means.

Therefore, even when the area values of each closed section are displayed in a table, the shape pattern of the closed section is displayed as a heading in association with the area value. It can be displayed and can be used for learning the integral.

According to a thirteenth aspect of the present invention, there is provided a graph display means for displaying a graph of a plurality of function formulas (for example, CPU 2, display unit 6 shown in FIG. 1, S1203 in FIG. 25, FIG. 26).
(A)) and a name creation unit (eg, CPU2 shown in FIG. 1; S1204 to S12 in FIG. 25) for creating a name for each closed section surrounded by the graphs of the plurality of functional expressions.
21) and name display means (for example, CP shown in FIG. 1) for displaying the name created by the name creation means by attaching it to each closed section displayed on the graph display means.
U2; S1222 in FIG. 25; FIG. 26 (B)).

According to the calculation apparatus of the thirteenth aspect, a graph of a plurality of function formulas is displayed by the graph display means, and a name is created for each closed section surrounded by the graph by the name creation means. The created name is displayed by being attached to each closed section by the name display means.

Therefore, the name is automatically created and displayed for each closed section, which can be used for learning of a graph using a computing device and learning of an integral such as obtaining the area of the closed section. .

According to a fourteenth aspect of the present invention, there is provided a graph display means for displaying a graph of a plurality of function formulas (for example, CPU 2 and display unit 6 shown in FIG. 1; S1306 to S130 in FIG. 27).
7; FIGS. 28 (B) and 28 (C)) and area value input means for inputting an area value (for example, input unit 3 shown in FIG. 1; S in FIG. 27).
1308 to S1309; FIG. 28D), and when the function formula includes an unknown variable, the area value of a closed section surrounded by the graphs of the plurality of function formulas is input by the area value input means. Variable value determination means (for example, CPU2 shown in FIG. 1; S1310 to S1311 in FIG. 27) for determining the value of the unknown variable so as to be equal to the area value.
FIG. 28 (E)).

According to the calculation device of the present invention, a plurality of function formula graphs are displayed by the graph display means, and when the area value is input by the area value input means, the function formula is unknown. When a variable is included, the area value of a closed section surrounded by the plurality of function formula graphs is
The value of the unknown variable is determined by variable value determination means so as to be equal to the input area value.

Therefore, the value of the unknown variable included in the function formula is determined according to the input area value, so that the function formula for obtaining the desired area value is easily confirmed together with the stepwise graph display. This makes it possible to use the present calculation apparatus for learning of a more advanced integral.

[0049]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIGS.
An embodiment of the computing device 1 according to the present invention will be described. In the computing device 1 according to the present embodiment, various modes can be selected by operating a mode key provided in the input unit, and the designated mode data is stored in the mode data memory 802 in the RAM 8. The processing program corresponding to the designated mode is read out from the storage medium 11, expanded in the RAM 8, and various processes are executed.

The processing modes that can be executed by the computer 1 of the present invention include a closed section trace mode (first embodiment; see FIGS. 3 and 4) and a range designation mode by pen instruction (second mode).
Embodiment, third embodiment; see FIGS. 5 to 8),
Integral range division display mode (fourth embodiment; see FIGS. 9 and 10), integration formula calculation mode (fifth embodiment; see FIGS. 11 and 12), replacement integral display mode (sixth embodiment) 13; FIG. 14; display erase mode other than the designated closed section (seventh embodiment; see FIGS. 15 and 16); closed section movement display mode (eighth embodiment; FIG. 1)
7, see FIG. 18), a closed section enlarged display mode (ninth embodiment; see FIGS. 19 and 20), a closed section number addition mode (tenth embodiment; see FIGS. 21 and 22), Closed section table display mode (eleventh embodiment; FIG.
24, a closed section name creation mode (twelfth embodiment; see FIGS. 25 and 26), an unknown variable calculation mode (thirteenth embodiment; see FIGS. 27 and 28), and the like. The processing in each processing mode will be described below separately for the first to thirteenth embodiments.

[First Embodiment] Hereinafter, a computer 1 according to a first embodiment of the present invention will be described with reference to FIGS.
Will be described in detail.

First, the configuration will be described. FIG. 1 is a block diagram showing a circuit configuration of a computing device 1 according to the present invention. This figure 1
In the computing device 1, the CPU (Central Processing)
Unit) 2, input unit 3, tablet 4, position detection circuit 5,
Display unit 6, display drive circuit 7, RAM (Random Access Me
mory) 8, ROM (Read Only Memory) 9, storage device 1
0 and the storage medium 11.

When the power of the computing device 1 is turned on, the CPU
2 reads out the initial display menu program stored in the ROM 9 and displays various displays based on the initial display menu program and the menu display of the processing mode on the display unit 6. Based on the mode instruction input via the input unit 3, the mode data is stored in the mode data memory 802 of the RAM 8, and the corresponding processing program is read out from the ROM 9 or the storage device 10 to read the R.
The processing is temporarily stored in the AM 8, and various processes based on the program are executed to centrally control the respective units of the computing device 1. That is, the CPU 2 executes various processes based on the read predetermined program, stores the processing results in the work memory 828 in the RAM 8, and displays the processing results on the display unit 6 via the display drive circuit 7. The processing result is stored in the storage device 1 based on an instruction input through the input unit 3.
0 in the storage medium 11.

In the first embodiment, the CPU 2 executes a closed section tracing process (see FIG. 3) described later as a process corresponding to the mode data. In the closed section tracing process (see FIG. 3), the CPU 2 converts the function formula data read out or input from the storage medium 11 into RA data.
Secured in the function formula data memory 803 set in M8,
Each graph data of the graph of these function formulas is generated and output to the display drive circuit 7, and the graph display screen 6a of the display unit 6
To be displayed.

Then, the CPU 2 detects a closed section surrounded by a plurality of function formula graphs, and stores the detected closed section data in the RAM 8. Further, when the closed section is designated by the operation of the trace key 3f of the input unit 3 and the operation of the up / down / left / right movement keys 3e, each time the designated operation is performed, the designated section in the graph displayed on the graph display screen 6a is designated. The display format of the closed section is changed and displayed. Also CP
U2 calculates the area value of the designated closed section, and displays the calculated area value on the graph display screen 6a.

In the present invention, a graph for forming a closed section is based on a continuous graph represented by a functional expression. However, even if a graph is represented by a functional expression, there is a function that becomes discontinuous, such as a graph of Y = 1 / X. For example, Y = X and Y = 1 /
Although the graph of X has two intersections, there is no closed section surrounded by the two points. Considering such a case,
In the detection of a closed section according to the present invention, the vertex of the graph is detected, and the presence of the vertex of the graph between the two intersections assumes that the graph is continuous between the two intersections. Do.

The input unit 3 includes a data input key 3a for inputting numerical values, characters, and the like included in the function expression, a mode key 3b for setting a processing mode, and an execution key 3c for inputting start instructions for various processes. , E for terminating the process
A keyboard composed of an XIT key 3d, up / down / left / right movement keys 3e, a trace key 3f for specifying a trace in a closed section, a graph execution key 3g for drawing a graph of a function expression, various function keys, and the like is provided. The key press signal is output to the CPU 2.

The tablet 4 is an input device in which a device for designating coordinates such as an input pen 4P and a plate-like device for sensing the designated coordinates are combined. The position detection circuit 5 uses an electromagnetic induction system, a magnetostrictive system, or the like. The position coordinates specified by the input pen 4P are detected based on a coordinate reading principle such as a pressure-sensitive method. The tablet 4 is integrated with a display unit 6 to be described later, and can perform an input operation by directly instructing an icon or the like displayed on the display unit 6 with the input pen 4P.

The display unit 6 is an LCD (Liquid Crystal Dis
play), and performs various displays based on a drive signal input from the display drive circuit 7. Display drive circuit 7
Generates a drive signal based on display data input from the CPU 2 and controls display of the display unit 6.

The RAM 8 temporarily stores designated application programs, input instructions, input data, processing results, and the like.

FIG. 2 is a diagram showing a memory configuration of the RAM 8. As shown in FIG. 2, the RAM 8 includes a display data memory 801 and a mode data memory as various memory areas for inputting input instructions, input data, processing results, and the like in various processes executed in the computing device 1 of the present invention. 802, function formula data memory 803, graph data memory 804, intersection data memory 805, vertex data memory 806, designated closed section data memory 807, detected coordinate number register 808, l register 809, m register 81
0, n register 811, area value data memory 812, integral expression data memory 813, coordinate position data memory 81
4, replacement mathematical expression data 815, replacement graph data memory 8
16, a post-replacement integral range data memory 817, a post-replacement integral expression data memory 818, a movement amount data memory 819, a post-transfer integral expression data memory 820, a display range data memory 821, a closed section physical quantity data memory 822, an area table memory 823, Graph name data memory 824, closed section name data memory 825, unknown function expression data memory 8
26, variable value data memory 827, work memory 82
8, etc.

The display data memory 801 stores data to be displayed on the display unit 6 as bitmap pattern data. The mode data memory 802 stores an initial display menu screen and mode setting data indicating a processing mode set by operating the mode key 3b of the input unit 3 during various processes.

The function formula data memory 803 stores one or a plurality of function formula data input from the input unit 3 on the function formula input screen 6c. The graph data memory 804 stores graph data for drawing a graph of the function expression data.

The intersection data memory 805 stores intersection coordinate data for intersections of a plurality of function equation graphs. The vertex data memory 806 stores vertex coordinate data for the vertices of the graph of each function expression.

The designated closed section data memory 807 stores closed section configuration graph data, intersection coordinate data or vertex coordinate data relating to the closed section currently designated by the input unit 3, dot data included in the closed section, and the like. It is memorized. The detected coordinate number register 808 stores detected coordinate number data which is the total number of intersections and vertices of the graph.

The l register 809, the m register 810, and the n register 811 are registers for storing numerical information of intersection coordinate positions or vertex coordinate positions forming a designated closed section when the closed section is designated by a trace. Each time the up / down / left / right movement key 3e of the input unit 3 is operated, any one of the l register 809, the m register 810, and the n register 811 is updated according to a predetermined order, and an intersection coordinate position or a vertex coordinate position for forming a closed section. Switch.

The area value data memory 812 stores area value data of a designated closed section. Integral expression data memory 8
13 stores integration formula data for obtaining the area value of the designated closed section. When the designated closed section has two or more integral ranges, integral expression data for each range, which is each integral expression, is also stored as integral expression data.

The coordinate position data memory 814 stores data indicating the coordinate position to be painted when the inside of the closed section is painted.

The permutation formula data memory 815 stores permutation formula data input from the input unit 3 when performing permutation integration. The replacement formula is a formula that indicates the relationship between a certain variable and a variable after replacement. Replacement graph data memory 816
Stores the graph data of the function formula after replacement converted by the replacement formula. Integration range data memory after replacement 8
17 stores the integration range data converted by the substitution formula. In the post-replacement integral expression data memory 818,
The integral expression data after the replacement is stored.

The moving amount data memory 819 stores the moving amount data in the x direction and the moving amount data in the y direction in the closed section.
Δx data and Δy data are stored, respectively. The post-movement integral expression data memory 820 stores integral expression data for the moved closed section.

The display range data memory 821 stores setting data for setting the relationship between the Xmax value, the Xmin value, the Ymax value, the Ymin value of the display range and the dot position.

The closed section physical quantity data memory 822 stores some physical quantities of the closed section, such as the order of the area value of each closed section, the order of the X-axis direction, the order of the Y-axis direction, and the like in association with the order.

The area table memory 823 stores an area table TBL in which an area value of a closed section is associated with dot pattern data obtained by symbolizing a dot pattern of the closed section.

The graph name data memory 824 stores graph name data of each function expression. The closed section name data memory 825 stores the created name data of each closed section.

The unknown function expression data memory 826 stores the unknown function expression data, which is a function expression including an unknown variable, input by the input unit 3. Variable value data memory 8
27 stores the value of the unknown variable calculated according to the area value.

The work memory 828 temporarily stores data input / output by the CPU 2 in accordance with control processing of various operation modes, designated application programs, input instructions, input data, processing results, and the like.

The ROM 9 stores a basic program corresponding to the computer 1. That is, it stores basic programs that do not need to be rewritten, such as an initial display menu program executed when the power of the computing device 1 is turned on, various function operation programs, and a processing program executed in each processing mode.

The storage device 10 has a storage medium 11 for storing programs, data, and the like.
Is composed of a magnetic or optical storage medium or a semiconductor memory. The storage medium 11 is fixedly provided in the storage device 10 or is detachably mounted. The storage medium 11 includes various processing programs, function formula data, and various processing programs corresponding to the computing device 1. And the like processed in step (1).

The program, data, and the like stored in the storage medium 11 may be configured to be received and stored from another device connected via a communication line or the like. A storage device having the storage medium 11 may be provided on another connected device side, and a program, data, and the like stored in the storage medium 11 may be used via a communication line.

Next, the operation will be described. FIG. 3 is a flowchart illustrating a closed section tracing process executed by the computing device 1 in the first embodiment. Also,
FIG. 4 shows the display unit 6 at each stage of the closed section trace processing.
FIG. 7 is a diagram for explaining a display example of the above and an example of operation of the input unit 3.

The computer 1 stores in the ROM 9 a program capable of selecting various modes via the input unit 3, and the closed section trace mode is selected by operating the mode key 3b of the input unit 3. And the CPU 2
A predetermined program is read from M9 or the storage medium 11, and a function formula input screen for inputting function formula data to be operated is displayed on the display unit 6 via the display drive circuit 7. When a plurality of function formula data is input to the function formula input screen in a predetermined format via the input unit 3, the plurality of function formula data input to the function formula input screen is converted to R
It is secured in the function formula data memory 803 of AM8 (step S101).

Thereafter, when the graph execution key 3g of the input unit 3 is operated (step S102), a graph display screen 6a, which is a screen for displaying the input function formula in a graph, is displayed on the display unit 6. An X-axis display 6x and a Y-axis display 6y are displayed on the graph display screen 6a.

The CPU 2 reads out the function formula data stored in the function formula data memory 803, generates graph data for displaying each function formula data in a graph, and stores the generated graph data in the graph data memory of the RAM 8. 804, and a graph of each function expression is displayed on the graph display screen 6a of the display unit 6 (step S10).
3: see FIG. 4 (A)).

FIG. 4A is a diagram showing an example of each graph displayed in the process of step S103. As shown in FIG. 4A, the graph display screen 6a of the display unit 6
Shows an X-axis display 6x and a Y-axis display 6y, and within the display range, graphs G1 and G
2 and G3 are displayed.

Next, when a closed section trace execution instruction is input by operating the trace key 3f of the input section 3 (step S104), the CPU 2 detects a closed section surrounded by the graph. That is, the intersection coordinates and vertex coordinates of each of the graphs G1 to G3 within the display range are detected (step S105). For example, regarding the graphs G1 to G3 in the display state of FIG. 4A, as shown in FIG.
Each intersection coordinate data of the intersections C1 to C6 is detected, and the vertex T
Each vertex coordinate data of 1 to T3 is detected. The detected intersection coordinate data and vertex coordinate data are stored in RAM, respectively.
8 intersection data memory 805, vertex data memory 806
Is stored. Further, the CPU 2 counts the total number of detected intersections and vertices (the number of detected coordinates K) and sets the numerical value in the detected coordinate number register 808 of the RAM 8. In this example, the value of the total number of the intersections C1 to C6 and the vertices T1 to T3 (detected coordinate number K) is set to “9” and set in the detected coordinate number register 808 (step S106).

Thereafter, the coordinates of the detected intersections and vertices are rearranged in the order of smaller x-coordinate values, and the RAM 8
In the detected coordinate table. In the example shown in FIG. 4B, the intersections C1 to C6 and the vertices T1 to T3 are “C1, C2, C3, T1, C4, T2,
T3, C5, and C6 are rearranged in this order and are secured in the detection coordinate table (step S107).

Thereafter, the CPU 2 extracts the three smallest points among the detected coordinates from the detected coordinate table (step S108). At this time, numerical values indicating the coordinates to be extracted are set in the l register 809, the m register 810, and the n register 811. At first, l = “1”, m =
Set as “2”, n = “3”. The numerical value set in each register is a numerical value indicating the order of smaller x-coordinate values of each detected point (the order secured in the detected coordinate table). That is, l = “1”, m = “2”, n =
When set as “3”, the intersection C1, the intersection C
2. The intersection C3 is set as coordinates surrounding the closed section.

Here, the CPU 2 sets the l register 809, m
It is determined whether or not the area determined by the values set in the register 810 and the n register 811 is a closed section (step S109). That is, it is determined whether each of the coordinates C1, C2, and C3 is surrounded by a continuous graph.

If it is determined that the graph is a continuous graph between the respective coordinates and is a closed section (step S109; Ye
s), with this closed section as a specified closed section, data of a specified closed section configuration graph which is a graph constituting the specified closed section,
The dot data included in the designated closed section is stored in the designated closed section data memory 807 of the RAM 8. Further, the designated closed section is displayed in solid color. What is fill display?
This means that colors and display formats are displayed in a display format different from that of other parts so as to be identifiable (step S110; FIG. 4).
(B)).

FIG. 4B is a diagram showing the graph display screen 6a in a state where the closed section E1 surrounded by the intersections C1, C2, and C3 is displayed in a solid color. As shown in FIG. 4B, a designated closed section E surrounded by C1, C2, and C3
1 is surrounded by continuous graphs G1, G2, G3. Further, the designated closed section E1 is displayed so as to be identifiable in a different color or display format from the other areas.

Further, the CPU 2 calculates an area value for the designated closed section E1. When calculating the area value, the function formula data of the graph constituting the designated closed section E1 is read from the function formula data memory 803, and the intersection C
An integral operation is performed on the function data read in the integral range determined by 1, C2, and C3 to obtain an area value (step S111). FIG. 4 shows the calculated area value s1.
It is displayed in the graph display screen 6a as shown in FIG.

Next, when it is determined in step S109 that the area determined by the coordinates indicated by the numerical values set in the l register 809, the m register 810, and the n register 811 is not a closed section (step S1).
09; No), or as an instruction to move the painted area in the graph,
e is operated (step S112), the CPU 2
Changes the value of the n register 811 to the next value that is not already specified and sets it. Here, the value of the n register 811 set to n = “3” is updated to n = “4” and set (step S113).

Further, the CPU 2 determines whether or not the updated value of the n register 811 is larger than the detected coordinate number K stored in the detected coordinate number register 808 of the RAM 8 (step S114). If it is smaller (Step S114; No), the process returns to Step S109, and it is determined whether the area surrounded by the intersection or the vertex indicated by the numerical value set in the l register 809, the m register 810, and the n register 811 is a closed section. Is determined,
If it is a closed section, the closed section is set as a designated closed section in the RAM 8
Is updated and stored in the designated closed section data memory 807, and the process of filling and displaying the inside of the designated closed section is repeated. further,
The area value of the designated closed section that has been painted and displayed is calculated and displayed in the graph display screen 6a. When an instruction to move the painted area is input from the input unit 3, the value of the n register 811 is updated and set.

As described above, the processing from step S109 to step S113 is repeated, and when the value of the n register 811 becomes larger than the detected coordinate number K (step S11).
4; Yes), and then update and set the value of the m register 810 to the next value not already specified as coordinates (step S115). At this point, the value of the m register 810 is updated from m = “2” to m = “3”. Further, it is determined whether the numerical value set in the m register 810 is larger than the detected coordinate number K (step S1).
16) If the number of detected coordinates is smaller than K (step S1)
16; No), and set the value of the n register 811 to the smallest value not set as coordinates (step S117). That is, the 1 register 809 is "1"
Since the m register 810 is set to “4”, the n register 811 is set to “2”.

Here, the flow shifts to step S109 again, and l
Register 809, m register 810, n register 811
It is determined whether or not the area determined by the value set in is a closed section. After that, if it is a closed section, the closed section is updated and stored in the RAM 8 as a designated closed section, and the designated closed section is painted out. Further, the area value of the designated closed section that is filled and displayed is calculated and the graph display screen 6a is displayed.
When an instruction to move the paint range is input from the input unit 3, the value of the n register 811 is updated and set, and whether or not the value of the n register 811 is larger than the number K of detected coordinates is determined. A determination is made (steps S109 to S114).

Steps S109 to S11
Step 4 is repeated until the value set in the n register 811 becomes larger than the number K of detected coordinates. n register 81
When the value set to 1 becomes larger than the detected coordinate number K,
Next, the processing of steps S115 to S117 is executed. That is, the value of the m register 810 is updated, and when the value of the m register 810 is equal to or smaller than the number of detected coordinates K, n
The value of the register 811 is updated, and steps S109 to S109 are performed.
Step S114 is repeated.

When the value of the m register 810 updated in step S115 becomes larger than the number of detected coordinates K (step S116; Yes), the value of the l register 809 is updated to the next value which is not already specified as a coordinate. And set (step S118). At this point, the value of the l register 809 is updated from l = “1” to l = “2”. Further, it is determined whether the numerical value set in the l register 809 is larger than the detected coordinate number K (step S119). If the numerical value is smaller than the detected coordinate number K (step S119; No), the m register 810 and the n register 811 is set to the smallest value not set as coordinates (step S120, step S120).
117). That is, since the l register 809 is set to “2” and the m register 810 is set to “3”, the value of the n register 811 is set to “4”.

Here, the flow shifts to step S109 again, and l
Register 809, m register 810, n register 811
It is determined whether or not the area determined by the value set in is a closed section. If it is a closed section, the specified closed section is updated and stored in the specified closed section data memory 807 as a specified closed section, and the inside of the specified closed section is displayed in solid color. Further, the area value of the designated closed section which is filled and displayed is calculated, and the area value is displayed in the graph display screen 6a. When an instruction to move the paint area is input from the input unit 3, the n register 81
The value of 1 is updated and set, and it is determined whether the value of the n register 811 is larger than the number K of detected coordinates (steps S109 to S114).

Steps S109 to S11
Step 4 is repeated until the value set in the n register 811 becomes larger than the number K of detected coordinates. n register 81
When the value set to 1 becomes larger than the number of detected coordinates K,
Steps S115 to S117 are executed. That is, the value of the m register 810 is updated. If the value of the m register 810 is equal to or smaller than the number of detected coordinates K, the value of the n register 811 is updated, and steps S109 to S114 are repeated.

Further, when the value set in the m register 810 becomes larger than the number of detected coordinates K, step S118
Through the processing of steps S120 and S117 to update and set the values of the l register 809, the m register 810, and the n register 811.

As described above, each time an instruction to move the paint area is input, the l register 809 and the m register 81
The values of the 0 and n registers 811 are sequentially updated and set, and it is determined whether or not the area determined by the values set in the respective registers is a closed section. If the area is a closed section, the area is painted out as a designated closed section. Then, the area value is calculated and displayed.

When the value set in the l register 809 is larger than the number of detected coordinates K (step S
119; Yes), the main closed section trace processing ends.

FIGS. 4 (B), (C), (D), (E)
It is a figure which shows the example of a display of the graph display screen 6a in the case of switching a designated closed area and performing solid display each time the right movement key 3e of the input part 3 is operated.

As shown in FIG. 4A, the graph display screen 6
When the closed section trace instruction is input by pressing the input unit 3 and the trace key 3f while the graphs G1, G2, and G3 are displayed in a, first, the l register 809 is set to "1" and the m register 810 is set to "1". 2 ″, n register 811
Is set to “3”, and as shown in FIG. 4B, the closed section E1 surrounded by the intersections C1, C2, and C3 is displayed as a designated closed section, and its area value s1 is set to “2.5”. Will be displayed as Thereafter, by operating the right shift key 3e of the input unit 3, the l register 809 is set to "1", the m register 810 is set to "4", and the n register 811 is set.
Is set to “5”, as shown in FIG. 4C, the closed section E surrounded by the intersections C1, T1, and C4
1 is displayed in solid color, and its area value s2 is “9.6”.
Will be displayed as

Further, by operating the right movement key 3e of the input unit 3, the 1 register 809 becomes "2" and the m register 81
When “0” is set to “4” and the n register 811 is set to “5”, as shown in FIG.
The closed section E3 surrounded by C4 is displayed in solid color, and its area value s3 is displayed as "7.1".

By operating the right movement key 3e of the input unit 3, the l register 809 is set to "5" and the m register 810 is set.
Is set to “7” and the n-register 811 is set to “8”, as shown in FIG.
The closed section E4 surrounded by 5 is displayed in solid color,
The area value s3 is displayed as “8.8”.

As described above, in the closed section tracing process executed in the first embodiment, a graph of the input function formula is displayed on the graph display screen 6a, and further, a closed section tracing instruction is input. Then, the CPU 2 detects the closed section by detecting the intersection coordinates and the vertex coordinates of each graph, and further sorts the detected coordinates in ascending x-coordinate value and stores them in the detection coordinate table of the RAM 8. .

[0108] The CPU 2 also specifies an intersection coordinate or a vertex coordinate for determining a closed section by an l register 809,
The values of the m register 810 and the n register 811 are updated and set, and it is determined whether or not the area surrounded by the points indicated by the l register 809, the m register 810, and the n register 811 is a closed section. If it is a closed section, the information on the specified closed section is stored in the specified closed section data memory 807 of the RAM 8, and all the dots included in the specified closed section are displayed so as to be identifiable and further displayed. The area value of the section is calculated, stored in the area value data memory 812 of the RAM 8, and displayed on the display unit 6.

Further, when an instruction to move the painted display range is input by an instruction of the up / down / left / right movement key 3e or the like,
Each time the operation is performed, the CPU 2 sequentially updates the values of the l register 809, the m register 810, and the n register 811, fills and displays the closed section determined by the value of each register as the designated closed section, and calculates the area value. To display.

Therefore, the closed section on the graph can be specified by a simple key operation, and the specified closed section is displayed in a solid color, so that it can be easily confirmed visually. In addition, since the area value of a specified closed section can be quickly confirmed together with the display of the closed section, it is effective for analysis of a graph and learning of area calculation by integration.

In the present embodiment, the area value for the designated closed section is calculated and displayed on the display unit 6. However, an integral expression for calculating the area value is calculated and the display unit 6 calculates the area value. May be displayed on the display unit 6, or both the integral expression and the area value may be displayed on the display unit 6.

In the above-described example, the instruction to move the paint range is input by operating the right shift key, and the order of movement is also in a closed section including a point having a small x-coordinate value (on the left side of the display unit). Is moved to a closed section including the point having a large x-coordinate value (right side of the display unit). However, the present invention is not limited to this. For example, the l register 809, the m register 810, and the n register If the setting value of 811 is updated so as to take a smaller value in order, it is possible to move from the right side of the display unit to the left side of the display unit. Furthermore, the operation of specifying the closed section can be performed more freely by combining the operation of the right movement key and the operation of the left movement key.

[Second Embodiment] Next, a second embodiment of the computer 1 to which the present invention is applied will be described with reference to FIGS.

In the first embodiment, the tracing instruction from the input unit 3 has been described as an example of a method of designating the closed section. In addition, as shown in the second embodiment, the display unit 6, a tablet 4 is provided integrally, and a dedicated input pen 4 is provided.
It is effective that the user directly paints and designates an arbitrary closed section on the graph displayed on the graph display screen 6a using P.

Further, when the range is designated by directly painting, it is often troublesome for the user to strictly paint the area in the closed section to every corner. The section is recognized as being specified.

Hereinafter, as a second embodiment, a paint range designation process (see FIG. 5) will be described. In addition,
Since the computing device 1 in the second embodiment is the same as that described in the first embodiment, the description of the configuration is omitted, and the same components are denoted by the same reference numerals and will be described below.

In the paint range designation process (see FIG. 5), the CPU 2 secures the function formula data read or input from the storage medium 11 in the function formula data memory 803 set in the RAM 8, and stores these function formulas. Each graph data of the graph is generated and output to the display drive circuit 7 to be displayed on the graph display screen 6a of the display unit 6. More CPU
2 detects the coordinate position data on the graph display screen 6a, which is directly instructed to the tablet 4 by the input pen 4P, by the position detection circuit 5, and displays the dot at the detected coordinate position by filling it out. Further, the CPU 2 determines how much the filled area occupies the closed section. When the filled area reaches a certain percentage or more, the closed section is designated and the designated closed section is determined. The section is determined, and all the dots in the specified closed section are automatically filled and displayed.

Next, the operation will be described. FIG. 5 is a flowchart illustrating a paint range specifying process executed by the calculation device 1 according to the second embodiment. FIG.
Indicates the display unit 6 at each stage of the filling range designating process.
7A and 7B are diagrams illustrating a display example of FIG. 6 and a state of an operation of painting a range on the tablet 4.

As in the case of steps S101 to S103 in the first embodiment, when a plurality of function formula data is input to the function formula input screen in a predetermined format via the input unit 3, the CPU 2 inputs the data. Of multiple function formula data
When the graph execution key 3g of the input unit 3 is operated (step S202), the CPU 2 stores the function formula data stored in the function formula data memory 803 in the function formula data memory 803 of the AM 8 (step S201). The graph data is read out to generate graph data for displaying each function formula data in a graph, the generated graph data is stored in the graph data memory 804 of the RAM 8, and the graph of each function formula is displayed on the graph display screen 6a of the display unit 6. (Step S203; see FIG. 6A).

FIG. 6A is similar to the display state shown in FIG. 4A described above, except that a transparent tablet 4 is provided on the graph display screen 6a. In FIG. 6A, the graphs G1, G2, G of the respective functional expressions are displayed within the display range of the graph display screen 6a together with the X-axis display 6x and the Y-axis display 6y.
3 is displayed.

When the coordinates within the closed section are painted out with the input pen 4P as a range designation instruction for the tablet 4 (step S204; see FIG. 6B), the CP
U2 obtains the filled coordinate position data detected by the position detection circuit 5, obtains the ratio of the filled area of the obtained coordinate position data to the whole closed closed section, and sets the ratio in advance. It is determined whether the predetermined ratio is reached (step S20).
5).

If the ratio of the filled area does not reach the predetermined ratio and the range is not determined (step S
205; No), it is determined whether or not a predetermined time has elapsed since the start of the filling input in the range (step S206). If the predetermined time has not elapsed (step S206; No) ), Step S2
The process returns to step 04, and further receives a fill input by the input pen 4P. When the ratio of the filled area reaches the preset ratio and the range is determined (step S2)
05; Yes) or, if the ratio of the filled area does not reach the preset ratio, but the predetermined time has elapsed (Step S206; Yes), the determined range is designated as the designated closed section, and this designation is performed. Information on the closed section (closed section configuration graph, intersection coordinate data, etc.) is stored in the specified closed section data memory 807, and the unfilled dots included in the specified closed section are filled (step S207). Further, the area value of the designated closed section is calculated,
The calculated area value is stored in the area value data memory 812 and displayed on the graph display screen 6a (step S208; see s5 in FIG. 6C).

After that, when a re-execution instruction is input (step S209; Yes), the paint is erased (step S210), the displayed area value is erased (step S211), and the state shown in FIG. It returns to the original graph display screen 6a in such a display state, and waits for the input of the paint range by the input pen 4P again.

If the re-execution instruction is not input after the range is specified by filling, the area value of the determined range is calculated, and displayed (step S209; No), the main filling range specifying process ends.

FIG. 6B is a diagram showing an example of a painting operation with a pen, and FIG. 6C is a diagram showing a state in which the entire designated closed section is painted.

As shown in FIG. 6A, when the graphs G1 to G3 of the function formulas are displayed on the graph display screen 6a, as shown in FIG. When the inside of the closed section E3 is painted out using 4P, the ratio of the area painted by the processing of steps S205 to S206 to the total number of dots in the closed section is obtained. Then, when the painted area is equal to or more than a predetermined ratio of the closed section, or when a certain time has elapsed,
Even during the painting, the range is determined, and FIG.
A closed section E3 which is a range determined as shown in (C).
, Dots that have not yet been painted are displayed as filled. The determined range E3 is set as the designated closed section, and its area value s5 is obtained and displayed.

As described above, in the second embodiment, with a graph of a plurality of functional expressions displayed on the graph display screen 6a, the closed section formed by the graph is integrated with the display screen. When the filling for the tablet 4 provided in is specified, all the dots in the range specified for filling are not painted, and the specified closed section is determined in a range equal to or more than a predetermined ratio or when a predetermined time elapses. Then, all the dots included in the closed section are displayed in a solid color. Further, the area value of the closed section is obtained and displayed on the display unit 6.

Therefore, when an arbitrary area on the graph is filled with the input pen 4P, the area is fixed when a certain percentage of the area is filled, and the closed section can be designated. Can be easily performed. Further, since it is not necessary to strictly fill all the dots in the range, the fill-in input can be simplified, and the range can be quickly specified.

In the second embodiment, in addition to calculating and displaying the area value of the designated closed section,
An integral formula for obtaining the area value may be calculated and displayed.

[Third Embodiment] Next, a third embodiment of the computer 1 to which the present invention is applied will be described with reference to FIGS.

As a mode for designating a closed section surrounded by a graph of a plurality of function formulas, a trace instruction from the input unit 3 is provided in the first embodiment, and the display unit 6 is provided integrally in the second embodiment. In the above description, the closed section is directly painted on the designated tablet 4 to designate the closed section. However, if any point in the closed section is designated by touching with a pen, the entire closed section including the designated coordinates is designated. It is effective to fill and display as a specified closed section.

When a plurality of closed sections are to be specified in combination, it is effective that the closed section specified previously can be additionally specified while the filled state is maintained. It is effective to display the sum of the area values of a plurality of closed sections added and designated each time.

Hereinafter, a closed section designation process using a pen (see FIG. 7) will be described as a third embodiment. The configuration of the computing device 1 according to the third embodiment is the same as that described in the first embodiment, and a description thereof will be omitted, and the same components will be denoted by the same reference numerals and will be described below. I do.

The computing device 1 according to the third embodiment has a
Similarly to the computing device 1 of the embodiment, the display unit 6 is provided with the tablet 4 integrally, and the CPU 2 performs a closed section designation process using a pen, which will be described later, as a process corresponding to the set mode data. (See FIG. 7).

In the closed section designation process using the pen (see FIG. 7), the CPU 2 secures the function formula data read or input from the storage medium 11 in the function formula data memory 803 set in the RAM 8, and stores these function formula data. Each graph data of the graph of the formula is generated and output to the display drive circuit 7,
It is displayed on the graph display screen 6a of the display unit 6. Further CP
U2 detects the coordinate position data of one point directly specified by the input pen 4P with respect to the tablet 4 by the position detection circuit 5, and determines the minimum closed section including the detected coordinate position. All dots in the closed section are displayed in solid color. Further, the area value of the designated closed section is calculated, stored in the area value data memory 812, and displayed on the display unit 6.

When an instruction to designate a closed section by the pen for the second time or later is input, the area value of the designated closed section is calculated and added to the area value already stored in the area value data memory 812 and stored. . The display unit 6 displays the area value obtained by adding the area values of the plurality of closed sections.

Next, the operation will be described. FIG. 7 is a flowchart illustrating a closed section designation process using a pen, which is executed by the computing device 1 according to the third embodiment. FIG. 8 is a diagram illustrating a display example of the display unit 6 at each stage of the closed section specifying process using the pen and a state of the closed section specifying operation using the pen.

As in the case of steps S101 to S103 of the first embodiment, when a plurality of function formula data are input to the function formula input screen in a predetermined format via the input unit 3, the input is made. A plurality of function formula data are secured in the function formula data memory 803 of the RAM 8 (step S30).
1) When the graph execution key 3g of the input unit 3 is operated (step S302), the CPU 2 reads out the function formula data stored in the function formula data memory 803, and
Graph data for displaying each function formula data as a graph is generated, the generated graph data is stored in the graph data memory 804 of the RAM 8, and a graph of each function formula is displayed on the graph display screen 6a of the display unit 6. (Step S303; see FIG. 8A).

FIG. 8A is similar to the display state shown in FIG. 4A, except that the tablet 4 is provided on the display screen 6a. In FIG. 8A, the X axis display 6x,
Along with the Y-axis display 6y, the graphs G1, G2, and G3 of the input function expressions are displayed in the display range of the graph display screen 6a.

Thereafter, when one point Z1 in the closed section is touched to the tablet 4 by the input pen 4P (step S304; see FIG. 8B), the CPU 2
Designated coordinates Z1 detected by the position detection circuit 5
Is obtained (step S305). Thereafter, the CPU 2 determines whether or not the designated coordinate Z1 is included in any closed section (step S306).

If the designated coordinate Z1 is not included in any of the closed sections (Step S306; No), an error message indicating that the closed section cannot be specified is displayed on the display unit 6 (Step S307). If the specified coordinate Z1 is included in the closed section (Step S306; Yes), the closed section including the specified coordinate Z1 is set as the specified closed section, and the closed section configuration graph and the intersection coordinate data of the specified closed section are set. And other information in the designated closed section data memory 8 of the RAM 8.
07, and all the dots in the designated closed section are displayed in solid color (step S308; FIG. 8).
(C)).

Thereafter, the CPU 2 calculates the area value of the designated closed section (step S309), and adds the calculated area value to the area value already stored in the area value data memory 812 and stores it (step S310). Then, the CPU 2 reads out the area value data stored in the area value data memory 812, and displays the area value in the graph display screen 6a (step S311; s6 in FIG. 8C).

Here, the state of the graph display and the designation operation of the closed section will be described with reference to FIG. FIG. 8A shows a graph display screen 6a in a state where a plurality of graphs are displayed.
FIG. 8B shows a graph display screen 6a shown in FIG.
FIG. 8C is a diagram showing an example of a graph display screen 6a displaying a designated closed section and its area value, in a state where coordinates in an arbitrary closed section are indicated by the input pen 4P.

In the state where graphs G1, G2, and G3 of a plurality of function formulas are displayed as shown in FIG. 8A by the processing of steps S301 to S303, FIG.
As shown in (B), using the input pen 4P, any point Z1
Is touched, the coordinates of the touch position are detected by the position detection circuit 5. Further, the CPU 2 determines whether or not the detected coordinates are coordinates existing in the closed section. For example, when the detected coordinates are in the closed section E4, FIG.
As shown in (C), the closed section E4 is displayed in solid color. Further, the area value s6 of the closed section E4 is calculated and displayed on the graph display screen 6a as "8.8".

The closed section E4 specified by the input pen 4P
Is displayed, and after the area value s6 is displayed, when the closed section is further re-executed by touching the pen (Step S312; Yes), the processing of Steps S304 to S311 is further repeated. Here, the filled display of the closed section designated by the previous designation operation is maintained, and the area value data stored in the area value data memory 812 is also maintained. The section is further displayed in solid color, and the area value obtained by adding the area value to the area value of the previously specified closed section is displayed.
When the designation operation by the pen touch is not executed again (Step S312; No), the closed section designation processing by the pen is ended.

As described above, in the third embodiment, the tablet is provided on the display screen of the display unit 6, and a plurality of function formula graphs are displayed on the graph display screen 6a and are surrounded by the graphs. When one point in the closed section to be specified is specified by the input pen 4P, the closed section including the specified point is detected and displayed in a solid color. Also,
The area value of the specified closed section is calculated and stored in the area value data memory 812. In the second and subsequent specification, the area value of the specified closed section is stored in the area value data memory 812. Is further added to and displayed. In that case, the filled display of the closed section designated before the previous time is maintained.

Therefore, the closed section can be specified by a simple operation of touching the pen with one point, so that it is possible to provide a calculation device which is easy for the user to use. Further, in the second and subsequent pen touches, it is possible to specify other closed sections in combination while maintaining the specification of the closed section specified by the previous pen touch. Since the sum of the area values is displayed, it is possible to easily analyze the closed sections of various combinations.

In the third embodiment, in addition to calculating and displaying the area value of the designated closed section,
An integral formula for obtaining the area value may be calculated and displayed.

[Fourth Embodiment] Next, FIGS.
A fourth embodiment of the computing device 1 to which the present invention is applied will be described with reference to FIG.

As described in the first to third embodiments, when a closed section is specified, the specified closed section may have two or more different integration ranges. For example, three graphs G1 and G as shown in FIG.
A graph G is included in a closed section E3 constituted by G2 and G3.
1 and graph G3 and the integral range and graph G
There are two integration ranges, ie, an integration range sandwiched between 2 and the graph G3. In the learning of the integral for obtaining the area value, a different integral equation is created for each integral range, and the area is calculated by summing the integral equations. Therefore, in the learning of mathematics using the calculation device 1, it is effective that the integral range is displayed so as to be easily recognized. Therefore, in the calculation device 1 according to the fourth embodiment, when a closed section has a plurality of integration ranges, each integration range is displayed in a different color or display format to facilitate recognition of the integration range. .

Hereinafter, as the fourth embodiment, an integral range division display process (see FIG. 9) will be described. The computing device 1 according to the fourth embodiment has the same configuration as that of the computing device 1 described in the first embodiment, and a description thereof will be omitted, and the same components will not be described in the first embodiment. The following description is given with the same reference numerals as those in the drawings shown in the embodiments.

In the integral range division display process (see FIG. 4), the CPU 2 secures the function formula data read or input from the storage medium 11 in the function formula data memory 803 set in the RAM 8, and these function formulas are stored. Is generated and output to the display drive circuit 7 to be displayed on the graph display screen 6 a of the display unit 6.

Further, as described in the first to third embodiments, when a closed section is designated by the input pen 4P for the trace or the tablet 4, the CPU 2 further has a plurality of integration ranges. In order to determine whether the specified closed section is formed from three or more function formula graphs, it is determined. When there are a plurality of integration ranges, the position where the x-coordinate value of the designated closed section is minimum (the left end of the closed section) is detected, and the range sandwiched by the graphs is painted in order from left to right. Then, when the integration range changes, that is, when the graph constituting the range changes, the color or display format of the fill is changed to further fill the range.

Next, the operation will be described. FIG. 9 is a flowchart illustrating an integral range division display process performed by the calculation device 1 according to the fourth embodiment. FIG.
FIG. 7 is a diagram showing a display example of the display unit 6 at each stage of the integral range division display processing.

As in the case of steps S101 to S103 of the first embodiment, when a plurality of function formula data is input to the function formula input screen in a predetermined format via the input unit 3, the input is made. A plurality of function formula data are secured in the function formula data memory 803 of the RAM 8 (step S40).
1) When the graph execution key 3g of the input unit 3 is operated (step S402), the CPU 2 reads out the function formula data stored in the function formula data memory 803, and
Graph data for displaying each function formula data as a graph is generated, the generated graph data is stored in the graph data memory 804 of the RAM 8, and a graph of each function formula is displayed on the graph display screen 6a of the display unit 6. (Step S403; see FIG. 10A).

FIG. 10A shows a graph display screen 6a in which the graphs G1, G2, and G3 of the respective functional expressions are displayed together with the X-axis display 6x and the Y-axis display 6y.

Thereafter, one of the closed sections is designated by specifying the closed section trace by operating the trace key 3f and the up / down / left / right movement keys 3e of the input section 3, filling the closed section by using the input pen 4P, or specifying the closed section by touching the pen. When specified (see FIG. 10B),
The CPU 2 stores, in the designated closed section data memory 807, dot position data within the designated closed section, closed section configuration graph data that is data relating to a graph constituting the closed section, and the like (step S404).

Here, when an instruction to divide and display the integral range is input (step S405), CPU 2 determines whether or not the designated closed section is surrounded by three or more function expression graphs (step S406). ). Designated closed section is 3
If not enclosed by one or more function expressions (step S
406; No), an error display indicating that split display cannot be performed is displayed on the display unit 6 because there is only one integration range in the closed section (step S407), and the process ends.

When the designated closed section is surrounded by three or more function expression graphs (step S406; Yes),
The coordinates having the smallest x-coordinate among the coordinates included in the designated closed section are extracted and stored as the coordinate position M in the coordinate position data memory 814 of the RAM 8 (step S408). Further, the CPU 2 checks the graph forming the closed section at the coordinate position M (step S409), and determines whether the current closed section configuration graph is different from the previous closed section configuration graph at the x coordinate position (step S409). Step S410).

If the closed section configuration graph at the current coordinate position M is different from the closed section configuration graph at the immediately preceding coordinate position, the integration range is different (step S410; Yes). It is changed (step S411). The CPU 2 paints the y coordinate range at the coordinate position M of the designated closed section with the changed paint color (step S412).

If the closed section configuration graph at the current coordinate position M is the same as the closed section configuration graph at the immediately preceding coordinate position and is the same, since the integration range is the same (step S410; No), the fill color is changed. The y-coordinate range at the coordinate position M of the designated closed section is filled with the same fill color as the previous fill color without changing (step S412).

Thereafter, the value of the coordinate position M is added by the coordinate value corresponding to one dot to be displayed, and the coordinate position data memory 81 is added.
4 (step S413), and the coordinate position M
Has reached the maximum x-coordinate position among the coordinates in the closed section (step S414; Yes), the process ends.
If the coordinate position M does not reach the maximum x coordinate position (step S414; No), the process returns to step S409, checks the closed section configuration graph at the dot position of the coordinate position M, and changes the fill color only when different. , The y coordinate range at the coordinate position M is painted out, and the coordinate position M
Is updated to the next coordinate position. This step S409
The processing from step S414 to step S414 is repeated, and when the filling of each integral range in the closed section ends, the integral range division display processing ends.

Here, display examples at each stage of the graph will be described with reference to FIG. FIG. 10A is a graph display screen 6a in which a plurality of graphs are displayed, and FIG.
FIG. 1A shows a state in which a closed section E3 including a plurality of integration ranges is designated on the graph display screen 6a of FIG.
0 (C) is a diagram showing a state in which display colors of each integration range are displayed in different colors.

In the state where graphs G1, G2, and G3 of a plurality of function formulas are displayed as shown in FIG. 10A by the processing of steps S301 to S303, FIG.
When a closed section E3 surrounded by the graphs G1, G2, and G3 is designated as shown in FIG.
8 to S414, the left end (the minimum x
From the (coordinate values), a closed section graph constituting the specified closed section is confirmed.

That is, in the x-coordinate range from the intersection C2 to the intersection C3 of the designated closed section E3, the closed section configuration graphs are the graphs G1 and G3. Therefore, this intersection C2
Is displayed in a uniform color or display format within the range of the intersection C3. Also, from the intersection C3 to the intersection C4 of the designated closed section E3.
In the x-coordinate range, the closed section configuration graph is the graph G2 and the graph G3. Therefore, the range from the intersection C3 to the intersection C4 is displayed in a different color or display format from the range from the intersection C2 to the intersection C3. Therefore, FIG.
As shown in FIG. 0 (C), the designated closed section E3 is displayed in a different color or display format in a range E3a from the intersection C2 to C3 and in a range E3b from the intersection C3 to C4. Can be easily identified.

As described above, in the fourth embodiment, when the designated closed section has two or more integral ranges, the CPU 2 fills in the closed section with a color to be filled for each integral range. Or, fill and display with different display formats.

Therefore, when performing learning for forming an integral expression for obtaining an area value for a closed section, the integral range can be easily confirmed on the graph display of the calculation device.
Learning efficiency can be improved.

[Fifth Embodiment] Next, FIGS.
A fifth embodiment of the computing device 1 to which the present invention is applied will be described with reference to FIG. In the fourth embodiment described above,
When the specified closed section has multiple integration ranges, by filling in different colors or display formats for each integration range,
Although an example in which the integral range in the closed interval is displayed so as to be easily identified has been described, in the fifth embodiment, when the designated closed interval has a plurality of integral ranges, the integral range for each integral range is further reduced. Create an integral expression (integral expression for each range), display the integral expression for the specified closed interval in the form of the sum of the integral expressions for each range, and change the display color of the integral expression for each range to the same fill color as the corresponding integral range. By displaying the colors in accordance with the colors, it is possible to easily confirm the correspondence between the integration range and the integration formula.

Hereinafter, as a fifth embodiment, an integral expression calculating process (see FIG. 11) will be described. The computing device 1 according to the fifth embodiment has the same configuration as that of the computing device 1 described in the first embodiment, and a description thereof will be omitted, and the same components will be described in the first embodiment. The following description is given with the same reference numerals as those in the drawings shown in the embodiments.

In the integration formula calculation process (see FIG. 11),
The CPU 2 secures the function formula data read or input from the storage medium 11 in the function formula data memory 803 set in the RAM 8, generates each graph data of the graphs of these function formulas, and sends it to the display drive circuit 7. Output and display 6
Is displayed on the graph display screen 6a. Further, the CPU 2
When a closed section is specified by the input pen 4P for the trace or the tablet 4, and an integral expression display instruction is input from the input unit 3, the intersection coordinates and the vertex coordinates of the closed section are detected. In order to determine whether or not there is a range, it is determined whether or not the designated closed section is formed by three or more intersections.

When there are a plurality of integration ranges, the position of the intersection of the designated closed section is designated by the value of the l register 809, and this l
The intersection at the position of the value “l” of the register 809 and “l +
A range-based integral formula for a range between the intersection at the position of 1 "is created and stored in the integral formula data memory 813.
Next, the value of the l register 809 is incremented, and similarly, a range integral equation between the intersection at the position of the value “l” of the l register 809 and the intersection at the position of “l + 1” is created. The data is additionally stored in the integral expression data memory 813. All the range integral expressions stored in this way are read out and displayed as an integral expression in the form of a sum. When the closed section is displayed in a different fill color for each integration range, the range-based integration formula corresponding to the integration range is displayed in a corresponding color.

Next, the operation will be described. FIG. 11 is a flowchart illustrating an integral expression calculation process performed by the calculation device 1 in the fifth embodiment. Also, FIG.
It is a figure showing the example of a display of indicator 6 in each stage of integration formula calculation processing.

As in the case of steps S101 to S103 of the first embodiment, when a plurality of function formula data is input to the function formula input screen in a predetermined format via the input unit 3, the input is made. A plurality of function formula data are secured in the function formula data memory 803 of the RAM 8 (step S50).
1) When the graph execution key 3g of the input unit 3 is operated (step S502), the CPU 2 reads out the function formula data stored in the function formula data memory 803, and
Graph data for displaying each function formula data as a graph is generated, the generated graph data is stored in the graph data memory 804 of the RAM 8, and a graph of each function formula is displayed on the graph display screen 6a of the display unit 6. (Step S503; see FIG. 12A).

FIG. 12A is a diagram showing an example of the graph display screen 6a on which the graphs G1, G2, and G3 of the respective functional expressions are displayed together with the X-axis display 6x and the Y-axis display 6y.

Thereafter, when the closed section is designated by operating the trace key 3f and the up / down / left / right movement keys 3e of the input section 3, the closed section is designated by the input pen 4P, or the closed section is designated by the pen touch. The CPU 2 stores the dot position data in the designated closed section, the closed section configuration graph data, and the like in the designated closed section data memory 807 (step S50).
Along with 4), the designated closed section is displayed in solid color (FIG. 1).
2 (B)). Here, when the designated closed section has two or more integration ranges, the designated closed section is displayed so as to be identifiable for each integration range, as described in detail in the fourth embodiment (FIG. 12 ( C)).

Further, when an instruction to display an integral equation is input from the input unit 3 (step S505), the CPU
2 detects the coordinates of the intersections and vertices of the graph constituting the designated closed section (step S506). If the designated closed section does not have three or more intersections (step S507;
No), a function formula of a graph continuously connecting the start point and the end point of the designated closed section is determined (step S508), and an integration formula is created from the function formula and an integration range determined from the coordinates of the intersection (step S509). ), Stored in the integral equation data memory 813 and displayed on the display unit 6.

If the designated closed section is composed of three or more intersections (step S507; Yes), the number of detected intersections is K
Is set in the detected coordinate number register 808 (step S
511). Further, "1" is set to initialize the l register 809 (step S512). And CP
U2 sorts the x-coordinate values of the intersections in ascending order and secures them in the detection coordinate table in the sort order (step S51).
3).

Thereafter, the CPU 2 determines a closed section configuration graph which is a graph continuously connecting the intersection where the sort order is the value “l” of the l register 809 and the intersection where the sort order is “l + 1” (step S514). The function formula of this graph is read from the function formula data memory 803, and the x-coordinate value of the intersection at which the l register 809 is "l" and the intersection at which "l + 1" is obtained is determined from the read function formula and the intersection coordinates. An integral formula for each range is created from the integral range (step S515). The range-based integral equation to be created is created in the form of the following equation (1).

[0179]

(Equation 1)

Here, "+" given at the end of the range-based integral formula is for creating an integral formula in the form of a sum with the following range-based integral formula.

The CPU 2 stores the range-based integration formula created based on the formula (1) in the integration formula data memory 813, increments the value of the l register 809 (l = l + 1),
It is determined whether or not the value is equal to the number of detected coordinates K (step S517). If the value “l + 1” obtained by incrementing the value of the l register 809 is smaller than the number of detected coordinates K (step S517; No), the l register 809 is set to “l + 1” (step S518).
The process proceeds to step S514, and the processes of steps S514 to S516 are repeated. That is, l register 8
A function of reading and reading the function formula of this graph and the intersection coordinates of each graph from the RAM 8 is determined, and the function formula of this graph and the intersection coordinates of each graph are determined. A range-based integration formula is created from the integration range determined from the formula and the intersection coordinates, and the created range-based integration formula is additionally stored in the integration formula data memory 813, and then the value of the l register 809 is incremented (l + 1). It is determined whether or not the value is equal to the number of detected coordinates K (step S517).

When the value “l + 1” obtained by incrementing the value of the l register 809 becomes the same as the number k of detected coordinates (step S517; Yes), the creation of the integral formula for the entire integral range of the designated closed section ends. The integration formula stored in the integration formula data memory 813 of the RAM 8 is displayed on the integration formula display screen 6b of the display unit 6 (step S51).
0; see FIG. 12 (D)), and terminates the integral formula calculation processing.

Next, a display example at each stage of the integral formula calculation processing will be described as a specific example with reference to FIG.

First, a plurality of function formulas are input by the user, and as shown in FIG.
G2 and G3 are displayed, and the displayed graphs G1 and G3 are displayed.
When any one of the closed sections surrounded by G2 and G3 is designated, the designated closed section is displayed in solid color. FIG. 12B shows a display example in a state where the designated closed section E3 is displayed in a solid color. This designated closed section E3
Has two integral ranges, a range sandwiched between the graphs G1 and G3 and a range sandwiched between the graphs G2 and G3. Therefore, as described in detail in the fourth embodiment, The closed section E3 is displayed in a different color for each integration range.

FIG. 12C is a diagram showing an example in which the designated closed section E3 displays the integral range E3a and the integral range E3b in different colors. If the specified closed section has a plurality of integration ranges in a state where the closed section is specified in this manner, steps S506 to S518 are performed.
By the processing of, a range-based integral formula is created for each integration range,
It is displayed on the integral expression display screen 6b.

FIG. 12D is a diagram showing the integral expression display screen 6b. FIG. 12D shows the integral equation EQ1. The integral equation EQ1 is expressed in the form of the sum of the range-specific integral equations EQ1a and EQ1b for each integral range. That is, in the range of −2 ≦ x ≦ −2 / 3,
Since the range is sandwiched between the graph G1 and the graph G3, the functional expression Y1 of the graph G1 and the functional expression Y3 of the graph G3
From this, the integral equation EQ1a shown in the following equation (2) is obtained. In the range of −2 / 3 ≦ x ≦ 0, the graph G2 and the graph G
3, the integral equation EQ1b shown in the following equation (3) is obtained from the function equation Y2 of the graph G2 and the function equation Y3 of the graph G3.

[0187]

(Equation 2)

(Equation 3)

The range-based integration equation EQ1a is displayed in the same color as the integration range E3a shown in FIG. 12C, and the range-based integration equation EQ1b is displayed in the same color as the integration range E3b shown in FIG. Is displayed.

As described above, in the fifth embodiment, when there are a plurality of integration ranges in the designated closed section,
The PU 2 reads out the integration range and the function of the closed interval configuration graph for each integration range from the RAM 8, creates an integration formula for each range, and sequentially stores it in the integration formula data memory 813. Further, each of the created integral formulas for each range is displayed in a color corresponding to the fill color for each integral range.

Therefore, since an integral expression can be created for each integral range and displayed in a color corresponding to the color of the integral range, the integral expression and the integral range can be visually recognized in the integral learning for obtaining the area value. It is possible to easily check the integration, and it is possible to improve the learning efficiency of the integration using the calculation device 1.

[Sixth Embodiment] Next, FIGS.
A sixth embodiment of the computing device 1 to which the present invention is applied will be described with reference to FIG. In the sixth embodiment, a description will be given of a process for displaying a graph and an integral expression that are effective when learning permutation integration. In the permutation integral, a variable included in the original integral expression is replaced with another variable to deform the integral expression and facilitate the operation of integration. In the sixth embodiment,
Allows you to enter a replacement formula for replacing variables, displays a graph of the function formula after replacement, displays the graph on the graph by replacing the integration range, and displays the integration formula after replacing the variable. This makes it possible to easily confirm the process of permutation integration in learning using the computing device 1.

Hereinafter, a permutation integration display process (see FIG. 13) will be described as a sixth embodiment. The sixth
Since the computing device 1 according to the second embodiment has the same configuration as the computing device 1 described in the first embodiment, a description thereof will be omitted, and the same components will be described in the first embodiment. The following description is given with the same reference numerals as those shown in the drawings.

In the permutation integration process (see FIG. 13), C
The PU 2 secures the function formula data read or input from the storage medium 11 in the function formula data memory 803 set in the RAM 8, generates graph data for each of these function formulas, and outputs the graph data to the display drive circuit 7. Is displayed on the graph display screen 6a of the display unit 6. Furthermore, CPU2
Indicates that the closed section is designated by the trace or the input pen 4P for the tablet 4, and the closed section is painted out and stored in the designated closed section data memory 807. When an integral equation display instruction is input from the input unit 3, an integral equation for the designated closed section is created and displayed.

Further, in the sixth embodiment, when a permutation / integration execution instruction is input, an input of a permutation formula for substituting a variable included in the function formula is accepted, and the permutation is performed according to the permutation formula. The graph of the function expression is updated and displayed, the integration range after replacement is displayed on the graph, and the integration expression after replacement is obtained and displayed.

Next, the operation will be described. FIG. 13 is a flowchart illustrating a replacement integral display process executed by the calculation device 1 in the sixth embodiment. FIG.
FIG. 5 is a diagram showing a display example of the display unit 6 at each stage of the permutation integration display process.

First, on the function formula input screen 6c as shown in FIG. 14A, step S1 of the first embodiment is performed.
01 to step S103, via the input unit 3,
When a plurality of function formula data is input to the function formula input screen 6c in a predetermined format, the input plurality of function formula data is secured in the function formula data memory 803 of the RAM 8 (step S601). When the graph execution key 3g is operated (step S602), the CPU 2 reads out the function formula data stored in the function formula data memory 803, and generates graph data for displaying each function formula data in a graph, The generated graph data is stored in the graph data memory 804 of the RAM 8, and the graph of each function is displayed on the graph display screen 6a of the display unit 6 (step S603; see FIG. 14B).

FIG. 14A shows an example of the function expression input screen 6c, and FIG. 14B shows an example of the graph display screen 6a. The graph display screen 6a shown in FIG. 14B has a function formula Y in the function formula input screen 6c shown in FIG.
A graph G4 corresponding to the following equation (4) input as 1 and a graph G5 corresponding to the following equation (5) input as the function equation Y2 are displayed.

[0198]

(Equation 4)

(Equation 5)

Thereafter, when the closed section is designated by operating the trace key 3f and the up / down / left / right movement keys 3e of the input unit 3, the closed section is designated by the input pen 4P, or the closed section is designated by the pen touch. The CPU 2 stores the dot position data within the designated closed section, the closed section configuration graph data, and the like in the designated closed section data memory 807 (step S60).
Along with 4), the designated closed section is displayed in solid color (step S605; see FIG. 14C). FIG. 14 (C)
Closed section E5 surrounded by graphs G4 and G5
Indicates that the image is filled and displayed.

Next, when an integral expression display execution instruction is input (step S606), the CPU 2 creates an integral expression for the designated closed section E5, stores it in the integral expression data memory 813, and displays it on the display unit 6. Yes (step S60
7; see FIG. 14 (D)). FIG. 14D is a diagram illustrating an example in which the graph for the designated closed section E5 and the integral equation EQ3 are displayed on the graph display screen 6a. Integral equation EQ
3 is represented by the following equation (6).

[0201]

(Equation 6)

[0202] When the graphs G4 and G5 for the function formulas Y1 and Y2 and the integration formula EQ3 for the designated closed section E5 are displayed in this manner, a permutation execution instruction is input from the input unit 3 (step S608). The CPU 2 redisplays the function expression input screen 6c as shown in FIG. 14 (E) (step S609), and further displays the function expression input screen 6c.
In step c, an input of a replacement formula is accepted (step S
610). The replacement formula is an equation for replacing a variable included in a previously input function formula with another variable,
For example, when replacing the variable x included in the previously input function expression with cosT, the substitution equation EQT1 is x = cosT.

In this example, the variable x is replaced with cosT in the function formulas Y1 and Y2.
1 is input for each of the function formulas Y1 and Y2.

When the graph execution key 3g is operated after the replacement formula is input (step S611), the CPU 2 performs a function formula replacement process (step S612). In this replacement processing, the function formula stored in the function formula data memory 803 is replaced with a variable according to the replacement formula EQT1 input in step S610 to display a graph of the replaced function formula or to display an integration range. Or a process of creating an integral expression after replacement.

The CPU 2 calculates the function expression Y1 shown in Expression (4),
The replacement expression EQT1 for the function expression Y2 shown in Expression (5)
, And generates graph data for the replaced function expression, stores it in the replacement graph data memory 816, and displays the replaced graph on the graph display screen 6a of the display unit 6 (step S613; FIG.
(See G6 and G7 in (F)). Further, the CPU 2 also recalculates the integration range according to the substitution formula (step S6).
14) The replaced integration range is stored in the replacement integration range data memory 817.

Thereafter, the CPU 2 determines whether or not integral calculation is possible for the function formula after replacement in the integrated range after replacement (step S615). If integral calculation is not possible, a replacement integral error display is displayed. It is displayed on the display unit 6 (step S616), and a re-execution instruction of the replacement integration is awaited. When the re-execution instruction is input (step S617), the process returns to step S609 and the subsequent steps, and the function expression input screen 6c is displayed. , Re-inputting the replacement formula, replacing the function formula according to the replacement formula, replacing the integration range, creating the graph data, and displaying the graph.

If it is determined in step S615 that the integration operation can be performed (step S615; Yes),
The calculation range of the displayed graph after replacement is painted out (step S618; see E6 in FIG. 14F), and a replacement integral expression is created from the replacement function expression and the replacement integration range. Integral expression data memory after replacement 81
8 and displayed on the graph display screen 6a displaying the graph after the replacement (step S61).
9; see FIG. 14 (G)).

FIG. 14F is a graph G showing the function formula after the replacement in which the integration range E6 after the replacement is displayed in a solid color.
6 and G7, and FIG. 14 (G) is a diagram showing a state in which a post-replacement integral equation EQ4 for the post-replacement integration range is displayed. The integral equation EQ4 after the replacement is given by the following equation (7).
It is represented by

[0209]

(Equation 7)

When the replacement integral expression or graph is displayed, the replacement integral display processing ends.

As described above, in the sixth embodiment, when the input of the replacement mathematical expression is received and the replacement mathematical expression is input, the CPU 2 executes the function stored in the function formula data memory according to the replacement mathematical expression. Replace the expression, generate the graph data and display it as a graph. In addition, the integrated range after the replacement is also recalculated, and the integrated range is displayed in the displayed graph of the function after the replacement by filling it. Further, C
PU2 obtains a post-replacement integral expression from the post-replacement function expression and the post-replacement integration range, and displays it on the display unit 6.

Therefore, it is possible to easily confirm the graph of the function formula after the replacement, the integration formula after the replacement, and the integration range after the replacement by the replacement formula, so that the process of the replacement integration can be stepwise and clearly defined. You can check. As a result, the efficiency of integral learning using the calculation device 1 can be improved.

[Seventh Embodiment] Next, FIGS.
A seventh embodiment of the computing device 1 to which the present invention is applied will be described with reference to FIG. In the seventh embodiment, as described in detail in the first to third embodiments, when a closed section surrounded by a plurality of graphs is designated, a graph display other than the designated closed section is displayed. A process of deleting and displaying only the designated closed section is executed.

Hereinafter, as a seventh embodiment, a display erasing process (see FIG. 15) other than the designated closed section will be described. The computing device 1 according to the seventh embodiment has the same configuration as that of the computing device 1 described in the first embodiment, and a description thereof will be omitted, and the same components will be described in the first embodiment. The following description is given with the same reference numerals as those in the drawings shown in the embodiments.

In the display erasing process other than the designated closed section (see FIG. 15), the CPU 2 secures the function formula data read out or input from the storage medium 11 in the function formula data memory 803 set in the RAM 8. For each of the function formulas, graph data is generated, output to the display drive circuit 7, and displayed on the graph display screen 6a of the display unit 6. Further, when the closed section is designated by the input pen 4P for the trace or the tablet 4 and the designated closed section display instruction is input, the CPU 2 once deletes the display of the graph display screen 6a, and the intersection and the closed section surrounding the designated closed section. The composition graph is detected, and only the closed section is displayed in solid color.

Next, the operation will be described. FIG. 15 is a flowchart illustrating a display erasure process performed by the computing device 1 in a region other than the designated closed section according to the seventh embodiment. FIG. 16 is a diagram showing a display example of the graph display screen 6a at each stage of the display erasing process other than the designated closed section.

First, step S10 of the first embodiment
When a plurality of function formula data is input in a predetermined format via the input unit 3 as in the case of 1 to step S103, the CPU 2
Secures the input plurality of function formula data in the function formula data memory 803 of the RAM 8 (step S701), and operates the graph execution key 3g of the input unit 3 (step S701).
702), read out the function formula data stored in the function formula data memory 803, generate graph data for displaying each function formula data in a graph, and store the generated graph data in the graph data memory 804 of the RAM 8 At the same time, a graph of each function is displayed on the graph display screen 6a of the display unit 6 (step S703; FIG. 16A).
reference).

FIG. 16A is a diagram showing a graph display screen 6a. On the graph display screen 6a shown in FIG. 16 (A), graphs G1, G2, and G3 corresponding to the input respective function expressions are displayed together with the X-axis display 6x and the Y-axis display 6y.

Thereafter, the closed section is specified by specifying the closed section trace by operating the trace key 3f and the up / down / left / right movement keys 3e of the input section 3, by specifying the closed section by using the input pen 4P, or by specifying the closed section by touching the pen. Then, the CPU 2 stores the dot position data within the designated closed section, the closed section configuration graph data, and the like in the designated closed section data memory 807 (step S7).
04). At this time, the designated closed section is displayed in solid color as shown in FIG.

FIG. 16B shows graphs G2 and G3.
Indicates a state in which the closed section E4 surrounded by is designated and filled and displayed.

Next, when a designated closed section display instruction is input (step S705), the CPU 2 sets the graph display screen 6a.
Is once deleted (step S706). Thereafter, the CPU 2 determines the designated closed section E4 from the data on the designated closed section stored in the designated closed section data memory 807.
Is detected (step S707), the intersection having the smallest x-coordinate value among the detected intersections is determined (step S708), and x of this intersection is determined.
The inside of the closed section at the x dot position which is the dot position corresponding to the coordinates and the x dot position next to it, that is, the y coordinate range sandwiched by the closed section configuration graph is displayed in black (step S709).

Thereafter, the CPU 2 determines whether or not the position of the x dot to be painted has passed the x coordinate value of the adjacent intersection, and if it has not passed the x coordinate value of the adjacent intersection (step S710; No), the CPU 2 further proceeds. The closed section at the next x dot position is displayed in solid color. As described above, in the processing from step S709 to step S710, the successive x
When the closed section at the dot position is painted over and passes the x coordinate value of the intersection (step S710; Yes), the function formula of the closed section configuration graph that determines the y coordinate range of the next closed section to be painted is changed (step S711). And CPU
2 determines whether or not the closed section has ended, and if the closed section has not ended (step S712; No), the process proceeds to step S709 and the subsequent steps, and based on the closed section configuration graph after the change, The sandwiched y coordinate range is sequentially painted. When the filling of the closed section is completed in this way (step S712; Yes; see FIG. 16C), a series of display erasing processes other than the designated closed section is ended.

FIG. 16C is a diagram showing a display example of a graph in a state where the display other than the designated closed section is deleted.

At steps S701 to S705, as shown in FIG. 16A, graphs G1, G2, G
3 is displayed, a closed section E4 is designated as shown in FIG. 16B, and further a designated closed section display instruction is input.
Once all the graph displays on the graph display screen 6a are erased, the intersection and the data of the closed section configuration graph relating to the designated closed section E4 are detected. In the example shown in FIG. 16B, the intersections of the designated closed section E4 are c4 and c5, and the closed section configuration graph is a graph G2 and a graph G3.

First, among the detected intersections c4 and c5, x
For the x dot position next to the dot position at the x coordinate position of the intersection c4 having the smaller coordinates, the y coordinate range sandwiched between the graphs G2 and G3 is filled. Then next to x
The y-coordinate range sandwiched between the closed section configuration graphs G2 and G3 for the dot position is painted out. As described above, the y coordinate range at the next x dot position is sequentially filled, and when the y coordinate range reaches the x coordinate value of the intersection c5 (see FIG. 16C),
Although the closed section configuration graph is changed, the closed section E4 specified here ends because the closed section E4 ends at the position of the intersection c5.

As described above, in the seventh embodiment, when a designated closed section display instruction is input after a closed section is designated, the CPU 2 once deletes the display on the display screen and then only displays the designated closed section. Is displayed in solid color.

Therefore, it is possible to display the specified closed section in an easily viewable manner.

[Eighth Embodiment] Next, FIGS.
An eighth embodiment of the computing device 1 to which the present invention is applied will be described with reference to FIG. In the learning of the integral for obtaining the area from the functional expression, parallel movement is often used. This is because by performing the parallel movement, it is possible to eliminate the minus portion in the Y-axis direction from the closed section, or to simplify the calculation by setting the start point and the end point of the integration range to 0.

Therefore, in the eighth embodiment, as described in detail in the seventh embodiment, the display other than the designated closed section is erased, and only the designated closed section is displayed as a graph. The display position of the designated closed section can be moved in parallel, and the integral expression of the designated closed section at the display position after the movement can be recalculated and displayed.

Hereinafter, as an eighth embodiment, a closed section movement display process (see FIG. 17) will be described. The computing device 1 according to the eighth embodiment has the same configuration as that of the computing device 1 described in the first embodiment, and a description thereof will be omitted, and the same components will be described in the first embodiment. The following description is given with the same reference numerals as those in the drawings shown in the embodiments.

In the closed section movement display processing (see FIG. 17), as described in detail in the seventh embodiment, the CPU 2 designates a closed section in the displayed graph and inputs a designated closed section display instruction. Then, the display other than the designated closed section is deleted. Then, when an integral expression display instruction is input, an integral expression for the designated closed section is calculated and displayed. Also,
When the up / down / left / right movement key 3e of the input unit 3 is operated, the designated closed section is moved up / down / left / right in parallel in accordance with the operation of the up / down / left / right movement key 3e. Further, the CPU 2
The amount of movement Δx in the x direction from the display position of the closed section after the parallel movement
And the movement amount Δy in the y direction are detected, and the detected x and y
The integral expression of the closed section at the current display position is recalculated from the movement amounts Δx and Δy in the direction and displayed.

Next, the operation will be described. FIG. 17 is a flowchart illustrating a closed section movement display process performed by the calculation device 1 according to the eighth embodiment. FIG.
FIG. 9 is a diagram showing a display example of a graph display screen 6a at each stage of the closed section movement display processing.

First, when a plurality of function formula data is input in a predetermined format via the input unit 3, the input plurality of function formula data is secured in the function formula data memory 803 of the RAM 8 (step S801). When the graph execution key 3g of the input unit 3 is operated (step S802), the CPU 2
Reads the function formula data stored in the function formula data memory 803, generates graph data for displaying each function formula data in a graph, and stores the generated graph data in the graph data memory 804 of the RAM 8. At the same time, it is displayed on the graph display screen 6a of the display unit 6 (step S803; see FIG. 18A).

FIG. 18A is a diagram showing the graph display screen 6a. The graph display screen 6a shown in FIG. 18A displays an X-axis display 6x, a Y-axis display 6y, and graphs G1, G2, and G3 corresponding to the respective functional expressions.

Thereafter, the closed section is designated by the operation of the trace key 3f and the up / down / left / right movement keys 3e of the input section 3, the closed section trace designation by the input pen 4P, or the closed section designation by the pen touch. Then, the CPU 2 stores the dot position data in the designated closed section, the data of the closed section configuration graph, and the like in the designated closed section data memory 807 (step S).
804). At this time, the designated closed section is displayed in solid color as shown in FIG.

FIG. 18B shows graphs G2 and G3.
Indicates a state in which the closed section E2 surrounded by is designated and filled and displayed. The designated closed section E2 is
In the range between the intersection c1 and the intersection c4, the closed section configuration graph G
2 and G3.

Next, when a designated closed section display instruction is input (step S805), the CPU 2 performs the processing of steps S706 to S712 described in detail in the seventh embodiment, and executes processing other than the designated closed section E2. The display is deleted, and only the designated closed section E2, which is painted out, is displayed on the graph display screen 6a in addition to the X-axis display 6x and the Y-axis display 6y (step S806; see FIG. 18C).

As shown in FIG. 18C, when an integral expression display instruction is input in a state where only the designated closed section E2 is displayed on the graph display screen 6a (step S807; Ye).
s), the CPU 2 calculates the maximum value x of the x coordinate value of the closed section from the intersections c1 and c4 of the closed section configuration graph of the designated closed section E2.
And the minimum value min is calculated (step S808). Then, the calculated maximum value max and minimum value m of the x coordinate are calculated.
In is set as an integral range, an integral equation EQ5 for the designated closed section E2 is calculated, and the calculated integral equation EQ5 is stored in the RAM 8
Is stored in the integral expression data memory 813 and displayed on the graph display screen 6a (step S809).

For example, in the example shown in FIG. 18D, the integral range of the designated closed section E2 is -√2 ≦ x ≦ 0 and is a range sandwiched between the graphs G2 and G3. From the function equation of the graph, an integral equation EQ5 shown in the following equation (8) is calculated.

[0240]

(Equation 8)

If there is no input of the integral expression display instruction in step S807 (step S807; No), or after the integral expression is displayed in the process of step S809, the designated close is performed by operating the up / down / left / right key 3e of the input unit 3. When a section movement instruction is input (step S81)
0), the CPU 2 changes the display position of the designated closed section in accordance with the operation of the up / down / left / right movement key 3e. For example,
The operation of the up-shift key moves the designated closed section by a predetermined number of dots in the upward direction, and the operation of the right-shift key shifts the designated closed section E2 by the predetermined number of dots in the right direction (step S811; see FIG. 18E). ).

FIG. 18E is a diagram showing a state in which the designated closed section E3 is moved and displayed by operating the up key and the right key. The designated closed section E2 is translated and the intersection c1 is moved to the position of the intersection c1 'and the intersection c4 is moved to the position of the intersection c4' and displayed.

Thereafter, when an integral expression display instruction is input (step S812), the CPU 2 determines the movement amounts Δx and Δy in the x-axis direction and the y-axis direction of the designated closed section E2, and determines the movement amounts Δx and Δy. Is transferred to the moving amount data memory 81
9 (step S813). Further, “(x−Δx)” is substituted for “x” included in all mathematical expressions such as a function formula of a closed section configuration graph relating to the specified closed section E2 stored in the specified closed section data memory 807 (step S8).
14). Similarly, “(y + Δy)” is substituted for “y”.

Thereafter, the CPU 2 performs a simplification process for displaying the expression in a concise manner, changes the expression to a concise notation (step S816), and sets x at the intersection of the functions constituting the closed section E2 after the movement. The minimum value min and the maximum value max of the coordinates are recalculated (step S817). Then, the integral expression after the movement of the closed section is recalculated, stored in the post-movement integral expression data memory 820 of the RAM 8, and displayed on the display unit 6 (step S818; see FIG. 18F).

FIG. 18F shows a state in which the closed section E2 after the movement and the integral equation EQ6 after the movement are displayed.
When the closed section E2 is moved by “ｘ2” in the x direction, the integration range is changed by the movement amount Δx = √2, and 0 ≦ x ≦
√2, and the post-movement integral equation EQ6 is represented by the following equation (9).

[0246]

(Equation 9)

As described above, when the integrated equation EQ6 after the movement is calculated and displayed, a series of closed section movement display processing ends.

As described above, in the eighth embodiment, when only the designated closed section is displayed, the input unit 3
When the up / down / left / right movement key 3e is operated, the designated closed section is displayed at a position shifted by a predetermined number of dots in parallel with the operation. Then, the movement amount Δx in the x direction and the y direction,
Δy is detected, and the integral formula of the designated closed section at the position after the parallel movement is calculated and displayed from the movement amounts Δx and Δy.

Therefore, regarding the parallel movement of the closed section frequently performed in the learning of the integral, the graph display after the parallel movement and the area calculation after the parallel movement can be easily confirmed. It can also be used for learning, and the range of use of the computing device 1 can be expanded.

[Ninth Embodiment] Next, FIGS.
A ninth embodiment of the computing device 1 to which the present invention is applied will be described with reference to FIG. In the ninth embodiment, when the designated closed section is enlarged and displayed, an example in which the set value of the display range is recalculated to solve the problem of the integration range mismatch between the integration range and the graph display, which has conventionally occurred. Will be described.

That is, the coordinate values within the display range are determined by how many dots are present in the graph display range in the horizontal direction. If the display range is determined to be a sharp value (a value that is not a fraction due to a fraction, etc.), the sharpest value is set for the minimum and maximum values of the display range, and the coordinate values between It is determined by how many dots are present in the graph display range in the direction.

For example, if the graph display range is -5 <X <5
When there are 100 dots in the graph display range, the value is "0.1" per dot, that is, the closed section displayed on the screen has a good value of 0.1 unit. However, for example, if there are 127 dots in the graph display range, "0.0787740157..." Per dot, and the coordinate value of the third dot from the left is "-4.842519."
685 ... ".

In such a case, when it is desired to show a closed section where the range starts from “−4.8” on a graph, the pointer is generally moved in units of dots. The value cannot be pointed. Therefore, in the present embodiment, when executing the enlarged function of the closed section, a point indicating the closed section (intersection of two graphs) is calculated, and the intersection coordinate value is a fraction when the closed section is enlarged and displayed. Recalculate the display range setting value so as not to output.

Hereinafter, as a ninth embodiment, a closed section integral range value holding zoom process (see FIG. 19) will be described. Note that the computing device 1 in the ninth embodiment has the same configuration as the computing device 1 described in the first embodiment, so that the description thereof will be omitted, and the same components will be described in the first embodiment. The following description is given with the same reference numerals as those in the drawings shown in the embodiments.

[0255] Closed section integral range value holding zoom processing (Fig. 19)
), The CPU 2 receives a plurality of function expressions, displays a graph of the function expressions, specifies a closed section on the graph, and further inputs an enlarged zoom instruction for the specified closed section. When the closed section is enlarged and displayed, the display range is determined so that the intersection dot position becomes the intersection coordinate value so that the integration range does not have an excess or deficiency with respect to the dot value. That is, the intersection of the closed section configuration graph is calculated, and the set value of the display range is corrected so that the coordinate value of the intersection does not show a fraction when the closed section is enlarged and displayed.

Next, the operation will be described. FIG. 19 is a flowchart illustrating a closed section integral range value holding zoom process executed by the calculation device 1 in the ninth embodiment.
FIG. 20 is a diagram illustrating a display example of the display unit 6 at each stage of the closed section integration range value holding zoom process.

First, when a plurality of function data is input in a predetermined format via the input unit 3, the input plurality of function data are secured in the function data memory 803 of the RAM 8 (step S901). When the graph execution key 3g of the input unit 3 is operated (step S902), the CPU 2
Reads the function formula data stored in the function formula data memory 803, generates graph data for displaying each function formula data in a graph, and stores the generated graph data in the graph data memory 804 of the RAM 8. In addition, the graph of each function expression is displayed on the graph display screen 6 of the display unit 6.
a (step S903; see FIG. 20A).

FIG. 20A is a diagram showing the graph display screen 6a. On the graph display screen 6a shown in FIG. 20A, graphs G1, G2, and G3 corresponding to the input respective function expressions are displayed in addition to the X-axis display 6x and the Y-axis display 6y.

When the closed section is designated by the operation of the trace key 3f and the up / down / left / right movement keys 3e of the input section 3, the closed section is designated by the input pen 4P, or the closed section is designated by touching the pen. The CPU 2 stores the dot position data in the designated closed section, the closed section configuration graph data, and the like in the designated closed section data memory 807 (step S904). At this time, the designated closed section is painted out as shown in FIG.

FIG. 20B shows graphs G2 and G3.
Indicates a state in which the closed section E2 surrounded by is designated and filled and displayed. The designated closed section E2 is
In the range between the intersection c1 and the intersection c4, the closed section configuration graph G2
And G3.

Next, when a closed section enlargement zoom instruction is input (step S905), the CPU 2 sets a point indicating the closed section E2 (intersection points c1 and c of the closed section configuration graphs G2 and G3).
4) is calculated, and a calculation is started to prevent the intersection coordinate value from displaying a fraction when the closed section is enlarged and displayed.

First, the CPU 2 stores the maximum value Ymax in the Y-axis direction of the closed section E2 in the display range data memory 821 as Yhmax. Similarly, the minimum value Ymin in the Y-axis direction of the closed section E2 is stored in the display range data memory 821 as Yhmin (step S906). Further CP
U2 is the start coordinate value Xs and end coordinate value X of the designated closed section E2.
e is calculated and stored in the display range data memory 821 (step S907). Further, the CPU 2 detects the number of dots W on the graph display screen 6a in the x-axis direction, and stores it in the display range data memory 821 (step S908).

Thereafter, the CPU 2 calculates the following formula (10) to calculate the display width Z per dot. Equation (1
In (0), the denominator is set to “W−8” in consideration of a case where a margin is provided for each of the left and right four dots.

[0264]

(Equation 10)

The display width Z per dot is calculated by the equation (10), and the following equations (11) and (12) are calculated to obtain the maximum value Xma of the display range in the x direction.
x and the minimum value Xmin are reset (step S91)
0).

[0266]

[Equation 11]

(Equation 12)

Further, the maximum value Yhmax and the minimum value Yhmin in the y direction of the closed section stored in the display range data memory 821 are read, and the following equations (13) and (14) are obtained.
Is calculated to obtain the maximum value Ymax of the display range in the Y direction,
The minimum value Ymin is reset (step S911).

[0268]

(Equation 13)

[Equation 14] Here, α is a margin of an appropriate size.

[0269] Enlarged graph data for the designated closed section E2 is generated in the display range reset based on the calculations in steps S910 and S911, and the enlarged graph is displayed again on the display unit 6 (step S912; FIG. C)).

FIG. 20C is a diagram showing a state where the designated closed section E2 is enlarged and displayed on the graph display screen 6a. In the case where the enlarged display is performed in this manner, conventionally, a deviation between the intersection coordinate value and the dot value occurs, and an accurate integration range cannot be obtained. However, in the ninth embodiment, By determining the display range so that the dot position of the intersection becomes the intersection coordinate value, even when displaying the coordinate value of the intersection c4 as shown in the lower column of FIG.
= 0 ”and“ y = 0 ”.

As described above, in the ninth embodiment, when an enlargement zoom instruction for a designated closed section is input, when displaying a closed section in an enlarged manner, the integration range is changed with respect to the dot value. The display range is determined so that the intersection dot position becomes the intersection coordinate value so that there is no excess or shortage. That is, the intersection of the closed section configuration graph is calculated, and the set value of the display range is corrected so that the coordinate value of the intersection does not show a fraction when the closed section is enlarged and displayed.

Therefore, the problem of mismatch between the intersection coordinates at the intersection position of the closed section and the graph display position can be solved, and more accurate graph display and integral calculation can be performed.

[Tenth Embodiment] Next, a tenth embodiment of the computer 1 to which the present invention is applied will be described with reference to FIGS. In the tenth embodiment, when a plurality of function formula graphs form a plurality of closed sections, each closed section is sorted in the order of larger area value, smaller order, smaller x coordinate, and smaller y coordinate. The number of a certain order such as a small order is added to each closed section and displayed, so that the graph can be easily analyzed.

Hereinafter, a numbering process (see FIG. 21) will be described as a tenth embodiment. The tenth
Since the computing device 1 according to the second embodiment has the same configuration as the computing device 1 described in the first embodiment, a description thereof will be omitted, and the same components will be described in the first embodiment. The following description is given with the same reference numerals as those shown in the drawings.

In the number adding process (see FIG. 21), C
The PU 2 receives a plurality of function formulas, displays a graph of the function formulas, and, when an instruction for numbering a closed section on the graph is input, determines a number to be assigned based on the amount. The setting screen 6d to be set is displayed on the display unit 6, and the number assigned here is calculated for each closed section and stored in the closed section physical quantity data memory 822 of the RAM 8 in the set order. Then, the graph is displayed again on the graph display screen 6a, and the assigned order is displayed inside or near each closed section.

Next, the operation will be described. FIG. 21 shows the tenth
9 is a flowchart illustrating a number adding process executed by the computing device 1 in the embodiment. Also, FIG.
It is a figure showing the example of a display of indicator 6 in each stage of number addition processing.

First, when a plurality of function formula data is input in a predetermined format via the input unit 3, the input plurality of function formula data is secured in the function formula data memory 803 of the RAM 8 (step S1001). When the graph execution key 3g of the input unit 3 is operated (step S1002), the CPU
2 reads out the function expression data stored in the function expression data memory 803, generates graph data for displaying each function expression data in a graph, and stores the generated graph data in the graph data memory 804 of the RAM 8 At the same time, a graph of each function expression is displayed on the graph display screen 6a of the display unit 6 (step S1003; see FIG. 22A).

FIG. 22A shows the graph display screen 6a. On the graph display screen 6a shown in FIG. 22A, graphs G1, G2, and G3 corresponding to the input function expressions are displayed in addition to the X-axis display 6x and the Y-axis display 6y.

When a numbering instruction for a closed section is input from the input unit 3 (step S1004), a setting screen 6d as shown in FIG. Setting screen 6
d is a screen for setting which physical quantity of each closed section is to be assigned a number. In the example shown in FIG. 22B, as the physical quantity candidate data, “area order: large” J1,
"Area order: small" J2, "X-axis direction order" J3, "Y-axis direction order" J4, and the like are displayed.
The cursor 6k is displayed so that any one of J4 can be selected.

On the setting screen 6d, a physical quantity to be assigned a number is selected from the physical quantity candidate data J1 to J4 (step S1006), and when the selection is confirmed by operating the execution key 3c (step S1007), the function expression Is detected (step S1).
008) For each detected closed section, an operation is performed on the set physical quantity (step S1009), and the physical quantity of each closed section is secured in the closed section physical quantity data memory 822 in the specified order (step S1010).

Subsequently, the graph G is displayed on the graph display screen 6a.
1, G2 and G3 are displayed again (step S1011),
Further, the order stored in the closed section physical quantity data memory 822 is displayed in each closed section of the graphs G1, G2, G3 (step S1012; see FIG. 22C).

FIG. 22C is a diagram showing an example in which closed sections numbered in descending order of area value are displayed. As shown in FIG. 22 (C), the number display B1 is displayed as “1” in the closed section having the largest area, and the number display B2 is displayed as “2” in the closed section having the second largest area value. Numbers B3 to B5 are displayed inside or near each closed section as "3", "4", and "5".

As described above, in the tenth embodiment, when a plurality of function expressions are input, the CPU 2
A setting screen 6 for displaying a graph of the function formula and setting an amount to be numbered when an instruction to number the closed section on the graph is input.
d is displayed on the display unit 6, and the number to be given the number set here is calculated for each closed section, and RA is set in the set order.
M8 is stored in the closed section physical quantity data memory 822, the graph is displayed again on the graph display screen 6a, and the order of the magnitude of the physical quantity of each closed section stored in the closed section physical quantity data memory 822 is determined for each closed section. Display inside or near.

Therefore, it is possible to easily analyze the order of the size of the plurality of closed sections, the size of the x-coordinate value, and the like for a plurality of closed sections. This makes it easy to visually confirm the relationship with physical quantities such as.

As described in the present embodiment, in the case where a closed section is designated by tracing in the above-described first embodiment after a number is assigned to a certain physical quantity for each closed section. The order specified by the trace may be the numerical order given here.

[Eleventh Embodiment] Next, an eleventh embodiment of the computer 1 to which the present invention is applied will be described with reference to FIGS.

When the area of a closed section is obtained and the area values are tabulated and displayed, there are no graph formulas, data memory names, or the like that serve as headings that make the meaning of the table easy to understand. Therefore, in the eleventh embodiment,
When a graph of a plurality of function formulas forms a plurality of closed sections, an area table showing, in association with a dot pattern obtained by symbolizing the shape of the closed section, an area value of each closed section and a dot pattern. Create and display.

Hereinafter, a closed section table display process (see FIG. 23) will be described as an eleventh embodiment. Note that the computing device 1 in the eleventh embodiment has the same configuration as the computing device 1 described in the first embodiment, so that the description thereof will be omitted, and the same components will be described in the first embodiment. The following description is given with the same reference numerals as those in the drawings shown in the embodiments.

In the closed section table display process (see FIG. 23), when a plurality of function expressions are input, the CPU 2 displays a graph for the function expressions. Then, when an instruction to display the area table for the closed section on the graph is input, all the closed sections are detected, the area value of each closed section is calculated, and a dot pattern indicating the shape of each closed section is created. , An area table in which the area value is associated with the dot pattern is created, and the area table memory 823 of the RAM 8 is created.
And an area table is displayed on the display unit 6.

Next, the operation will be described. FIG.
9 is a flowchart illustrating a closed section table display process executed by the calculation device 1 according to the embodiment. Also,
FIG. 24 is a diagram illustrating a display example of the display unit 6 at each stage of the closed section table display processing.

First, when a plurality of function formula data are input in a predetermined format via the input unit 3, the input plurality of function formula data are secured in the function formula data memory 803 of the RAM 8 (step S1101). When the graph execution key 3g of the input unit 3 is operated (step S1102), the CPU
2 reads out the function expression data stored in the function expression data memory 803, generates graph data for displaying each function expression data in a graph, and stores the generated graph data in the graph data memory 804 of the RAM 8 At the same time, the graph of each function expression is displayed on the graph display screen 6a of the display unit 6 (step S1103; see FIG. 24A).

FIG. 24A shows the graph display screen 6a. The graph display screen 6a shown in FIG. 24 (A) displays graphs G1, G2, and G3 corresponding to the input respective function expressions, in addition to the X-axis display 6x and the Y-axis display 6y.

When an instruction to display the area table of the closed section is input from the input unit 3 (step S1104), the CPU 2
First, all closed sections surrounded by the graphs G1, G2, and G3 are detected (step S1105), the area value of each closed section is calculated, and the area table memory 8 of the RAM 8 is calculated.
23 (step S1106). Then CPU
2 creates a dot pattern DP in which the shape of each closed section is symbolized, and stores it in the area value table memory 823 in association with the previously stored area value for each closed section (step S1107). When the area value table TBL is created in this way, the area value table TBL is displayed on the display unit 6 (step S1108; FIG. 24).
(B)).

FIG. 24B shows a display example of the area value table TBL. In the example shown in FIG. 24B, the dot pattern D indicating the closed section E8 in FIG.
P1 and its area value s7 “13.1” are displayed in association with each other, the dot pattern DP2 indicating the closed section E7 and its area value s8 “10.0” are displayed in association with each other, and the closed section E9 is displayed.
And its area value s9 "8.
8 ”is displayed in association with the dot pattern DP4 indicating the closed section E6 and its area value s10“ 7.1 ”is displayed in association with each other. The area value table TBL is, for example, sorted and displayed in descending order of the area value.

As described above, in the eleventh embodiment, when a plurality of function expressions are input, the CPU 2
Display a graph for the function expression. Then, when an instruction to display the area table TBL for the closed section on the graph is input, all the closed sections are detected, the area value of each closed section is calculated, and a dot pattern DP indicating the shape of each closed section is created. Then, an area table TBL in which the area value is associated with the dot pattern DP is created and stored in the area table memory 823 of the RAM 8, and the area table TBL is displayed on the display unit 6.

Therefore, even when the area value of each closed section is tabulated and displayed, the dot pattern indicating the shape of the closed section is displayed as its heading in association with the area value, so that the meaning is easy to understand at a glance. An area table can be created and displayed.

[Twelfth Embodiment] Next, a twelfth embodiment of the computing device 1 to which the present invention is applied will be described with reference to FIGS. In the twelfth embodiment, a closed section surrounded by a plurality of function expression graphs is displayed with a name corresponding to the graph name.

Hereinafter, a closed section name creation process (see FIG. 25) will be described as a twelfth embodiment. In addition,
The computing device 1 according to the twelfth embodiment has the same configuration as that of the computing device 1 described in the first embodiment, and a description thereof will be omitted, and the same components will be described in the first embodiment. The same reference numerals as those shown in FIG.

In the closed section name creation processing (see FIG. 25), when a plurality of function expressions are input, the CPU 2 displays a graph for the function expressions. When an instruction to assign a name to a closed section on the graph is input, all closed sections are detected, and a closed section name is created for each closed section based on the name of the closed section configuration graph, and the corresponding closed section is created. To be displayed. When giving a name to a closed section, for example, among the intersections forming the closed section, the one having the smallest X coordinate is selected, and the graph name of the graph having the largest Y coordinate value among the graphs emerging from the intersection is given. A closed section name is created in the order of the first character of the closed section and the second largest character as the second character. Particularly when the closed section is made up of a circle or an arc, a clearer naming is performed by adding a circle or arc symbol to the end of the closed section name. If the same name has existed before, a single number is added after the name to prevent confusion between the names.

Next, the operation will be described. FIG.
9 is a flowchart illustrating a closed section name creation process performed by the calculation device 1 according to the embodiment. FIG.
6 is a diagram showing a display example of the display unit 6 at each stage of the closed section name creation process.

First, when a plurality of function formula data are input in a predetermined format via the input unit 3, the input plurality of function formula data are secured in the function formula data memory 803 of the RAM 8 (step S1201). When the graph execution key 3g of the input unit 3 is operated (step S1202), the CPU
2 reads out the function expression data stored in the function expression data memory 803, generates graph data for displaying each function expression data in a graph, and stores the generated graph data in the graph data memory 804 of the RAM 8 At the same time, a graph of each function expression is displayed on the graph display screen 6a of the display unit 6 (step S1203; see FIG. 26A).

FIG. 26A shows the graph display screen 6a. The graph display screen 6a shown in FIG. 26 (A) displays graphs G1, G2,
G3 is displayed. The graph G1 is given a name “A” as a graph name, the graph G2 is given a name “B”, and the graph G3 is given a name “C” in advance by a user setting. Is stored.

When a closed section naming instruction is input from input unit 3 (step S1204), CPU 2 detects all closed sections and stores the detected number of closed sections H (step S1205). Further, the counter C for counting the number of the closed section currently being processed is initialized to “1” (step S1026).

The CPU 2 starts creating a name for the closed section of the number set in the counter C. It is assumed that the numbers of the closed sections are determined, for example, as the first and second sections from the closed section having the intersection with the small X coordinate.
First, a name is determined for the “1” th closed section.
The “1” th closed section is the closed section E1 in the example shown in FIG.

The CPU 2 determines whether or not the closed section E1 is composed of three or more intersections (step S12).
07) If there are three or more, a closed section name is created by a normal naming method described later (steps S1208 to S1214). Since the closed section E1 for which a name is currently being created is a closed section including three intersections c1, c2, and c3, a normal name is assigned (step S120).
7; Yes).

In the usual way of naming, the closed section E1 is
The graph name of the graph G3 extending to the top at the smallest intersection c1 of the X coordinate is “C”, the graph G2 extending to the next at the intersection c1 is “B”, and the graph name of the graph G2 is extended from the intersection c2. Since the graph name of the present graph G1 is "A", "CBA" is created as the closed section name HN1 (step S1208).

After that, the CPU 2 refers to the closed section name data memory 825 of the RAM 8 (step S1209),
It is determined whether the same closed section name has already been created and stored (step S1210). If the same closed section name has been created previously (step S12
10; Yes), and the closed section name data memory 8
The same closed section name stored in No. 25 has number information j.
Is determined (step S121).
1). The number information j is a number added to prevent confusion of each closed section name when the same closed section name is created because the closed section configuration graph is the same even in different closed sections, This number is added to the end of the closed section name, such as “1”, “2”,.

When the number information j is added to the same closed section name stored in the closed section name data memory 825 (step S1211; Yes), the determined closed section ("CBA" in the above example) At the end of the number information "j +
1 "(step S1212).

When the same closed section name stored in the closed section name data memory 825 is not added with the number information j (step S1211; No), the stored closed section name is stored as “number information j”. "1" (step S1213), and "2" as the next number information j + 1 to the determined closed section name (step S1214).
Each is stored in the closed section name data memory 825 (step S1215).

If it is determined in step S1210 that the same closed section name has not been created before (step S1210; No), step S1211 is executed.
The created closed section name is stored in the closed section name data memory 825 without going through the processing of Step S1214 (Step S1215).

Thereafter, the CPU 2 determines whether or not the value of the counter C is equal to the detected number H of the closed section (step S1216). If there remains a closed section for which is not created (step S1216; No), the value of the counter C is incremented (C = C + 1; step S1).
217), a name is created for the closed section of the number set in the counter C (steps S1207 to S1215).

At step S1207, the counter C
Is determined not to have three or more intersections (step S1207; N
o) Further, it is determined whether or not the closed section is a circle or an ellipse (step S1218). If the closed section is a circle or an ellipse (Step S1218; Yes), how to name the circle or the ellipse (Step S121)
In 9), create a name. That is, in the case of a circle or an ellipse, a closed section name is obtained by adding a circular symbol to the graph name of a graph indicating a circle or an ellipse.

If the closed section is not a circle or an ellipse but consists of two intersections and vertices (step S12).
20), how to name when having vertices (step S1)
At 221), a name is created. In other words, when a vertex is present, a symbol with an arc shape is added (HN in FIG. 26B).
4) is a closed section name.

[0314] The name of each closed section is created in any of the usual way of naming, the way of naming a circle or an ellipse, or the way of having a vertex, and the created closed section is created. Name is closed section name data memory 8
When the creation of the names for all the closed sections is completed (step S1216; Yes), the CPU 2
Are graphs G1 and G1 displayed on the graph display screen 6a.
A corresponding closed section name is displayed inside or near each closed section formed by G2 and G3 (step S1222; see FIG. 26B).

For a closed section for which a closed section name cannot be created by any of the normal naming method, the naming method for a circle or an ellipse, or the naming method for a vertex, see step S1220; ), An error message indicating that the name cannot be created is displayed (step S)
1223), the main closed section name creation processing ends.

FIG. 26 (B) is a diagram showing an example of the graph display screen 6a in a state where a closed section name based on the graph name is created and added to each closed section and displayed.

The closed section E1 is composed of a graph G3 having a graph name “C”, a graph G2 having a graph name “B”, and a graph G1 having a graph name “A”.
A closed section name HN1 called “BA” is created and the closed section E1 is created.
Is displayed in addition to the vicinity of. In addition, the closed section E2
Is the graph G3 of the graph name "C" and the graph name "A"
And a graph G2 with a graph name "B", a closed section name HN2 called "CAB" is created and additionally displayed inside the closed section E2.

Similarly, the closed section E3 has the graph name “B”
, A graph G1 with a graph name “A”, a graph G1 with a graph name “C”, and a graph G2 with a graph name “B”, a closed section name “NAC3” called “BACB” is created. It is additionally displayed inside the closed section E2. Since the closed section E4 is a closed section including two intersections and vertices, the graph names “B” and “C”
A name obtained by adding an arc-shaped symbol to the end of the name “BC” created from the above is the closed section name HN4, and is displayed inside the closed section E4.

As described above, in the twelfth embodiment, when a plurality of function expressions are input, the CPU 2
Display a graph for the function expression. When an instruction to give a closed section name for a closed section on the graph is input, all closed sections are detected, and for each closed section, a normal naming method, a naming method for a circle or an ellipse, a vertex A closed section name is created in any of the ways of naming in the case of having, and is stored in the closed section name data memory 825.

In the usual naming method, a closed section name is created based on the graph name of the closed section configuration graph. If the same name has already been created, number information is added to the name to prevent confusion. In the case of naming a circle or an ellipse, a graph name with a circular symbol is the closed section name, and in the case of having vertices, the graph name is with an arc-shaped symbol. Is a closed section name.

When the closed section name is created, the CPU 2 adds the created closed section name to the corresponding closed section and displays it.

Therefore, the name is automatically created and displayed for each closed section, so that when learning the graph using the calculation device 1 or when learning the integral such as finding the area of the closed section. It is effective for

[Thirteenth Embodiment] Next, a thirteenth embodiment of the computer 1 to which the present invention is applied will be described with reference to FIGS. In the thirteenth embodiment, when an area value is further input when a function expression including an unknown variable is input, a closed area surrounded by a graph of another function expression and a graph of the function expression including the unknown variable is used. A process for determining the value of the unknown variable is performed so that the section has the same area value.

Hereinafter, an unknown variable calculation process (see FIG. 27) will be described as a thirteenth embodiment. Note that the computing device 1 in the thirteenth embodiment has the same configuration as the computing device 1 described in the first embodiment, and thus description thereof will be omitted, and the same components will not be described in the first embodiment.
The following description is given with the same reference numerals as those in the drawings shown in the embodiment.

In the unknown variable calculation process (see FIG. 27), when the function expression Y2 and the function expression Y1 including the unknown variable are input, the CPU 2 causes the graph of the function expression Y1 to be displayed within the graph display range. The unknown variable is temporarily determined, and the function formula Y
2 is displayed as a solid line, and the graph of the function formula Y1 is displayed as a broken line. When an area value of a closed section generated by being surrounded by the graph of the function equation Y1 and the graph of the function equation Y2 is input, the unknown variable of the function equation Y1 is set so that the closed section has this area value. Is calculated, the calculated unknown variable is displayed, and the graph of the function formula Y1 is displayed again with a solid line using the calculated unknown variable.

Next, the operation will be described. FIG.
6 is a flowchart illustrating an unknown variable calculation process executed by the calculation device 1 in the embodiment. FIG. 28
5 is a diagram showing a display example of the display unit 6 at each stage of the unknown variable calculation process.

First, when the function formula data of the function formula Y2 not including the unknown variable is input in a predetermined format to the function formula input screen 6c as shown in FIG.
The CPU 2 secures the input function expression data in the function expression data memory 803 of the RAM 8 (step S130).
1). Similarly, when the function formula data of the function formula Y1 including the unknown variable is input to the function formula input screen 6c in a predetermined format, the input function formula data is secured in the unknown function formula data memory 826 ( Step S1302).

FIG. 28A is a diagram showing an example of the function expression input screen 6c in a state where the function expressions Y1 and Y2 have been input. For example, the function expression data of the function expression Y2 not including the unknown variable is input by the following expression (15), and the function expression data of the function expression Y1 including the unknown variable is expressed by the following expression (16).
Is assumed to have been entered.

[0329]

(Equation 15)

(Equation 16) A: Unknown variable

When the input of the function expression is completed and an instruction to execute an unknown variable operation is input from the input unit 3 (step S1).
303), the CPU 2 checks the display range of the graph display screen 6a (step S1304), provisionally determines the value of the unknown variable A of the function formula Y1 from the size of the display range, and secures it in the variable value data memory 827 of the RAM 8. (Step S130
5). Thereafter, the CPU 2 generates graph data of the function expression Y2 that does not include the unknown variable, and displays the graph G8 on the graph display screen 6a (step S1306; FIG. 28).
(See (B)), the graph data of the function formula Y1 in which the value of the unknown variable is tentatively determined is generated, and the graph G9 is additionally displayed as a broken line on the graph display screen 6a (step S1).
307; FIG. 28 (C))

FIG. 28B is a graph G8 of the function formula Y2.
Is an example of a graph display screen 6a in which is displayed as a solid line, and FIG. 28C is a diagram showing an example of a graph display screen 6a in which a graph G9 of the temporarily determined function formula Y1 is additionally displayed as a broken line. .

When a display range in which the graph G8 of the function formula Y2 is displayed in an appropriate size is determined as shown in FIG. 28B, a graph of the function formula Y1 is further displayed within this display range. The value of the unknown variable A is provisionally determined so that it can be performed. At the stage where the processing up to step S1307 is completed, as shown in FIG. 28 (C), the state may not be a closed section constituted by the two graphs G8 and G9.

Next, the CPU 2 sets the graph display screen 6
An area value input area 6e for inputting an arbitrary area value is displayed in a (step S1308; FIG. 28D).
reference). Further, when an arbitrary area value is input to the area value input area 6e via the input unit 3 (step S1).
309) Calculate the value of the unknown variable A such that the closed section E10 generated by the graph G8 of the function formula Y2 and the graph G9 of the function formula Y1 becomes equal to the value of the input area value, and calculate the variable value data. The variable value stored in the memory 827 is updated and stored (step S1310).

Thereafter, if the CPU 2 determines that there is no real number solution in the variable value calculation process (step S1311; No), an error display indicating that the unknown variable A corresponding to the input area value does not exist is displayed. The information is displayed on the unit 6 (step S1312), and the unknown variable calculation process ends.

When it is determined that a real number solution exists for the unknown variable A (step S1311; Yes), the calculated value of the unknown variable is displayed on the graph display screen 6a, and the function expression Y1 including the unknown variable A is displayed. The graph G9 is displayed again. At this time, the graph G9 is displayed as a solid line (step S1313). Further, the closed section corresponding to the input area value is displayed in solid color (step S1314;
FIG. 28E).

Further, when a plurality of unknown variable values satisfying the conditions are calculated, and setting is made to display a graph for all the patterns, or when such an instruction is input (step S1315; Yes) ),
The display of the graph of the function formula Y1 and the fill display of the closed interval are deleted, the value of the unknown variable stored in the variable value data memory 827 is updated, and the function expression Y1 is updated with the updated value of the unknown variable. Is displayed as a solid line, and the closed section corresponding to the input area value is displayed in solid color.

When the display of all the values of the unknown variables satisfying the conditions is completed (step S1316; Ye)
s), the unknown variable calculation process ends.

As shown in FIG. 28D, when an area value is input to the area value input area 6e as, for example, “S = 1.8”, the graph G8 and the graph G9 are processed by the processing in step S1310. An unknown variable A is determined such that the closed section surrounded by {circle around (1)} obtains the area value “1.8”. Further, the value of the determined unknown variable A is determined in step S13.
As shown in FIG. 28E, for example, “A = 0.5” is displayed in the variable display area 6f by the process of FIG. 28, and the graph G9 is displayed again according to the value of the unknown variable. , The area value is “1.8”
Is closed and displayed.

As described above, in the thirteenth embodiment, when the function formula Y2 and the function formula Y1 including the unknown variables are input, the CPU 2 displays the graph of the function formula Y1 in the graph display range. The values of the unknown variables are provisionally determined as described above, and the graph of the function formula Y2 is displayed by a solid line, and the graph of the function formula Y1 is displayed by a broken line. When an area value of a closed section generated by being surrounded by the graph of the function equation Y1 and the graph of the function equation Y2 is input, the unknown variable of the function equation Y1 is set so that the closed section has this area value. Is calculated, the calculated unknown variable is displayed, and the graph of the function formula Y1 is displayed again with a solid line using the calculated unknown variable.

Therefore, the value of the unknown variable included in the function formula is determined according to the input area value, and the function formula for obtaining the desired area value is easily confirmed together with the stepwise graph display. This makes it possible to use the calculation device 1 for learning of a more advanced integral.

[0341]

According to the first and fifteenth aspects of the present invention,
A desired closed section on the graph can be quickly specified by a simple operation without performing an operation such as inputting an integration range.
Also, the specified closed section is displayed in a solid color, so that it can be easily visually confirmed, which is effective for learning graphs and integration.

According to the second aspect of the present invention, the closed section can be designated by handwriting on the graph display, so that the operation of designating the closed section becomes easier. Further, since it is not necessary to strictly paint all of the inside of the closed section, the painting work can be simplified and the range can be quickly specified.

According to the third aspect of the present invention, the area value of a closed section specified by a simple specifying operation can be quickly confirmed together with the display of the closed section, which is effective for learning a graph and area integration. .

According to the fourth aspect of the present invention, each time a designation operation is performed, another closed section can be designated while the designation of the closed section designated last time is maintained, so that a plurality of closed sections can be easily designated. Will be able to do it. In addition, since the sum of the area values for a plurality of closed sections is displayed, analysis of various combinations of closed sections can be easily performed, which is effective in learning.

According to the fifth aspect of the present invention, an integral expression for obtaining an area value for a closed section specified by a simple specifying operation can be quickly confirmed together with the display of the closed section, so that a graph or an integral Effective for learning.

According to the invention of claim 6, the integral range within the closed interval can be easily confirmed on the graph display of the computing device, and each integral expression for each integral range can be confirmed. Can clearly show the process of seeking
This is effective for learning integrals.

According to the seventh aspect of the present invention, it is possible to easily confirm the graph of the replaced functional expression, the integrated expression after the replacement, and the integrated range after the replacement by the replacement mathematical expression. It is possible to clearly confirm the calculation process unique to the integration step by step.

According to the eighth aspect of the present invention, it is possible to display the specified closed section in an easily viewable manner.

According to the ninth aspect of the present invention, it is possible to easily confirm the graph display after the parallel movement and the calculation of the area after the parallel movement for the parallel movement of the closed section frequently performed in the learning of the integral. Therefore, it can be used for learning a special calculation method, and the range of use of the calculation device can be expanded.

According to the tenth aspect of the present invention, it is possible to eliminate inconsistency between the coordinate values in the integral range of the closed section and the graph display position, and to perform more accurate graph display and integral calculation.

According to the eleventh and sixteenth aspects,
For a plurality of closed sections, the order of the area size, x
Analysis of the magnitude relationship of a predetermined amount such as the size of a coordinate value can be easily performed, and the relationship between a graph and a predetermined amount such as an area can be easily confirmed in learning of integration using a calculation device.

According to the invention of claims 12 and 17,
When displaying the area value of each closed section in a table,
Since the shape pattern of the closed section is displayed as its heading in association with the area value, a table that is easy to understand at a glance can be created and displayed, which can be useful for learning of integration.

According to the invention of claims 13 and 18,
Since the name is automatically created and displayed for each closed section, it can be useful for learning a graph using a computing device or learning an integral such as finding the area of the closed section.

According to the invention of claims 14 and 19,
Since the value of the unknown variable included in the function expression is determined according to the input area value, the function expression for obtaining the desired area value can be easily confirmed together with the step-by-step graph display. The present calculation device can be used for learning the developed integral.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a circuit configuration of a computing device 1 of the present invention.

FIG. 2 is a diagram showing a memory configuration of a RAM 8;

FIG. 3 is a flowchart illustrating a closed section tracing process executed by the calculation device 1 in the first embodiment.

FIG. 4 shows a display unit 6 at each stage of the closed section trace processing.
FIG. 7 is a diagram for explaining a display example of the above and an example of operation of the input unit 3.

FIG. 5 is a flowchart illustrating a paint range specification process executed by a calculation device 1 according to the second embodiment.

6 is a diagram illustrating a display example of the display unit 6 at each stage of a paint range specifying process, and a state of an operation of painting a range on the tablet 4. FIG.

FIG. 7 is a flowchart illustrating a closed section designation process using a pen, which is executed by the calculation device 1 according to the third embodiment.

FIG. 8 is a diagram illustrating a display example of a display unit at each stage of a closed section specifying process using a pen, and a state of a closed section specifying operation using a pen.

FIG. 9 is a flowchart illustrating an integral range division display process performed by the calculation device 1 according to the fourth embodiment.

FIG. 10 is a diagram showing a display example of a graph display screen 6a at each stage of the integral range division display processing.

FIG. 11 is a flowchart illustrating an integral expression calculation process executed by a calculation device 1 according to the fifth embodiment.

FIG. 12 is a diagram showing a display example of a graph display screen 6a and an integral equation display screen 6b at each stage of the integral equation calculating process.

FIG. 13 is a flowchart illustrating a permutation integration display process performed by a calculation device 1 according to a sixth embodiment.

FIG. 14 is a diagram showing a display example of a graph display screen 6a and a function expression input screen 6c at each stage of the permutation integration display processing.

FIG. 15 is a flowchart illustrating a display erasure process other than a designated closed section executed by the calculation device 1 according to the seventh embodiment.

FIG. 16 is a diagram showing a display example of a graph display screen 6a at each stage of a display erasing process other than a designated closed section.

FIG. 17 is a flowchart illustrating a closed section movement display process executed by the calculation device 1 according to the eighth embodiment.

FIG. 18 is a diagram showing a display example of a graph display screen 6a at each stage of the closed section movement display processing.

FIG. 19 is a flowchart illustrating a closed section integral range value holding zoom process executed by the calculation device 1 in the ninth embodiment.

20 is a diagram illustrating a display example of the display unit 6 at each stage of the closed section integration range value holding zoom process. FIG.

FIG. 21 is a flowchart illustrating a numbering process performed by the computing device 1 according to the tenth embodiment.

FIG. 22 is a diagram showing a display example of a graph display screen 6a and a setting screen 6d at each stage of the number adding process.

FIG. 23 is a flowchart illustrating a closed section table display process executed by the calculation device 1 according to the eleventh embodiment.

24 is a diagram illustrating a display example of the display unit 6 at each stage of the closed section table display processing. FIG.

FIG. 25 is a flowchart illustrating a closed section name creation process executed by the calculation device 1 in the twelfth embodiment.

FIG. 26 is a diagram showing a display example of a graph display screen 6a at each stage of a closed section name creation process.

FIG. 27 is a flowchart illustrating an unknown variable calculation process executed by the calculation device 1 in the thirteenth embodiment.

FIG. 28 is a diagram showing a display example of a graph display screen 6a and a function expression input screen 6c at each stage of an unknown variable calculation process.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Computing apparatus 2 CPU 3 Input part 4 Tablet 5 Position detection circuit 6 Display part 7 Display drive circuit 8 RAM 9 ROM 10 Storage device 11 Storage medium

Claims (19)

[Claims] 1. A graph display means for displaying a graph of a plurality of function formulas; a designating means for designating one of closed sections surrounded by the graphs of the plurality of function formulas; A display control means for changing and displaying the display format of the specified closed section each time it is specified. 2. The designating means includes: a filling designation means for designating the closed section by hand-painting on the graph displayed on the graph display means; 2. The calculation device according to claim 1, further comprising: a specification determination unit that determines the specification of the closed section when the ratio is equal to or more than a predetermined ratio of the closed section. 3. An area value calculating means for calculating an area value of a closed section specified by the specifying means, and an area value displaying means for displaying the area value calculated by the area value calculating means. The computing device according to claim 1, wherein: 4. When a plurality of closed sections are designated by a plurality of designation operations by said designation means, said display control means includes:
While retaining the previously specified closed section display format,
The display format of the newly designated closed section is changed and displayed, and the area value calculating means adds the area value of the newly designated closed section to the area value of the previously designated closed section. 4. The calculating device according to claim 3, wherein the sum of the area values of the plurality of designated closed sections is calculated. 5. An integral expression calculating means for obtaining an integral expression for calculating an area value of a closed section specified by said specifying means, and an integral expression displaying means for displaying the integral expression calculated by said integral expression calculating means. The computing device according to claim 1, further comprising: 6. The integration formula calculating means, wherein the specified closed section has a plurality of integration ranges,
A range-integral formula calculating means for calculating a range-specific integral formula for each integral range, wherein the integral formula display means displays the range-specific integral formula calculated by the range-specific integral formula calculating means; 6. The computing device according to claim 5, wherein the control unit further changes and displays the display format of the closed section to a different display format for each of the integration ranges. 7. A replacement formula input means for inputting a replacement formula for replacing a variable included in the function formula with another variable, and the function formula based on the replacement formula input by the replacement formula input means. A post-replacement function formula operation means for obtaining a post-replacement function expression by replacing a variable included therein, A post-replacement display control unit for changing a display format of a post-replacement integration range corresponding to the closed section specified by the specifying unit in the graph displayed on the post-replacement graph display unit; A post-replacement integral expression calculating means for calculating the post-replacement integral expression for the section; and a post-replacement integral expression displaying the post-replacement integral expression calculated by the post-replacement integral expression calculating means. Computing apparatus according to claim 1, characterized in that further comprising a shows means. 8. The display control means further comprises: display erasing means for erasing a graph display excluding a portion constituting the specified closed section when the specifying section specifies the closed section. The computing device according to claim 1, wherein: 9. A movement display control means for displaying the designated closed section in parallel translation, a movement amount detecting means for detecting a movement amount of the closed section, and a movement amount detected by the movement amount detecting means. A post-movement integral equation calculating means for calculating an integral equation for the closed section after the moving, and a post-moving integral equation displaying means for displaying the post-moving integral equation calculated by the post-moving integral equation calculating means. The computing device according to claim 8, further comprising: 10. A graph enlargement display means for enlarging a closed section designated by said designation means and displaying it within a display range, and integrating said closed section when enlarging and displaying said closed section by said graph enlargement display means. The calculation device according to claim 1, further comprising: a correction unit configured to correct the display range so as to eliminate a mismatch between the coordinate value of the range and the display position. 11. A graph display means for displaying a graph of a plurality of function formulas; a number calculation means for obtaining a number indicating a magnitude relationship of a predetermined amount for each closed section surrounded by the plurality of function formula graphs; A number display means for displaying the number obtained by the number calculation means by attaching the number to each of the closed sections. 12. A graph display means for displaying a graph of a plurality of function expressions; a shape pattern generation means for generating a shape pattern of each closed section surrounded by the plurality of function expression graphs; An area value calculation unit for calculating an area value; and a table in which, for each of the closed sections, a shape pattern created by the shape pattern creation unit and an area value calculated by the area value calculation unit are created. A computing device, comprising: table creation means; and table display means for displaying a table created by the table creation means. 13. A graph display means for displaying a graph of a plurality of function expressions; a name generation means for generating a name for each closed section surrounded by the plurality of function expression graphs; And a name display means for displaying the name added to each closed section displayed on the graph display means and displaying the closed section. 14. A graph display means for displaying a graph of a plurality of function expressions, an area value input means for inputting an area value, and when the function expression includes an unknown variable, a graph of the plurality of function expressions is used. Variable value determining means for determining the value of the unknown variable so that the area value of the enclosed closed section is equal to the area value input by the area value input means. . 15. A storage medium storing a computer-executable program, wherein the computer-executable program code for displaying a plurality of function formula graphs is surrounded by the plurality of function formula graphs. Program code that can be executed by a computer to specify any of the closed sections that have been set, and a computer that can change and display the display format of the specified closed section each time a closed section is specified. A storage medium characterized by storing a program including: 16. A storage medium storing a computer-executable program, wherein the computer-executable program code for displaying a plurality of function formula graphs is surrounded by the plurality of function formula graphs. A computer-executable program code for obtaining a number indicating a magnitude relationship of a predetermined amount for each closed section, and a computer-executable program for displaying the obtained number attached to each closed section and displaying the number A storage medium storing a code and a program including: 17. A storage medium storing a computer-executable program, wherein the computer-executable program code for displaying a plurality of function formula graphs is surrounded by the plurality of function formula graphs. A computer-executable program code for creating a shape pattern of each closed section, a computer-executable program code for calculating the area value of each closed section, and the shape for each closed section. A computer-executable program code for creating a table that associates the pattern with the area value; and a computer-executable program code for displaying the created table. A storage medium characterized by the above-mentioned. 18. A storage medium storing a computer-executable program, wherein the computer-executable program code for displaying a plurality of function formula graphs is surrounded by the plurality of function formula graphs. A computer-executable program code for creating a name for each closed section, and a computer-executable program code for displaying the created name for each of the closed sections. A storage medium storing a program. 19. A storage medium storing a computer-executable program, wherein the computer-executable program code for displaying a plurality of function formula graphs and the computer for inputting an area value are executed. Possible program code, and when the function expression includes an unknown variable, the area value of the closed section surrounded by the graphs of the plurality of function expressions is equal to the input area value. A storage medium storing a program including: a computer-executable program code for determining a value;