CN205451606U - Mathematics definite integral model - Google Patents
Mathematics definite integral model Download PDFInfo
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- CN205451606U CN205451606U CN201521095149.9U CN201521095149U CN205451606U CN 205451606 U CN205451606 U CN 205451606U CN 201521095149 U CN201521095149 U CN 201521095149U CN 205451606 U CN205451606 U CN 205451606U
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- definite integral
- mathematics
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- rectangle
- scale
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Abstract
The utility model discloses a mathematics definite integral model belongs to higher mathematics teaching aid technical field, the glass frame body is made by five transparent glass, wholly is the rectangular plate body form that does not have the closing cap in the top, and its inside gap is the rectangle intermediate layer, and the rectangle intermediate layer is thinner relatively, and stretch out from the top of glass frame body on rectangle intermediate layer top, leads to with the external world, can put into the fine sand in the rectangle intermediate layer, at the back of glass frame body, correspond rectangle intermediate layer department and be carved with the regional net of full wafer, be carved with horizontal scale in glass frame body back net below, be carved with fore -and -aft scale on glass frame body back net right side, the unit scale of horizontal and fore -and -aft scale aligns with the horizontal longitudinal line of net. Can be specifically the show definite integral nature of image, nature directly perceived is strong, economy is suitable for, portable, but the wide application is in definite integral classroom teaching.
Description
Technical field
This utility model relates to a kind of mathematics definite integral model, belongs to higher mathematics teaching aid technical field.
Background technology
At present, higher mathematics is a more difficult course, and the concept comprised, character, proposition, theorem etc. are the most abstract, bad understanding, and in the teaching of higher mathematics, teaching aid application is the most few.Definite integral knowledge therein is an important component part of higher mathematics, has application in a lot of fields more.Such as: the burn surface area of burn patient determines, optimal synthetism curve radian etc. is sought in the link of skeleton.In order to allow student be better understood from the study stage, grasp property of definite integral and application definite integral knowledge, this utility model provides a kind of mathematics definite integral model teaching aid.
Summary of the invention
This utility model provides a kind of mathematics definite integral model, is made up of clear glass, and centre is provided with rectangle interlayer, put into fine sand in interlayer, Irregular Boundary Surface can be formed, by grid and the scale at back, convenient observation size, calculate, rock to fine sand end face smooth, the rectangular area after deformation can be immediately arrived at, it is easy to carry, showing property of definite integral visually, intuitive is strong, economic and practical.
This utility model solves the technical scheme that its technical problem is used: a kind of mathematics definite integral model, it is made up of instrument bezel support body, rectangle interlayer and fine sand, instrument bezel support body is made up of five clear glasses, overall in top without the rectangular panel body shape of capping, its internal gap is rectangle interlayer, and rectangle interlayer is relatively thin, and rectangle interlayer top is stretched out from the top of instrument bezel support body, lead to the external world, fine sand can be put in rectangle interlayer；The back side at instrument bezel support body, the grid of entire area it is carved with at corresponding rectangle interlayer, being carved with horizontal scale below the grid of the instrument bezel support body back side, be carved with longitudinal scale on the right side of the grid of the instrument bezel support body back side, the unit scales of horizontal and vertical scale aligns with the transverse and longitudinal line of grid.
The beneficial effects of the utility model are: this utility model solves in the teaching of current higher mathematics, model teaching aid application is less, and does not has the problem of teaching aid in terms of definite integral knowledge, the displaying property of definite integral of concrete image, intuitive is strong, economic and practical, it is simple to carry, can be widely applied to the classroom of the character of definite integral, with in the education activities of property of definite integral, be conducive to exciting the divergent thinking of student, the beneficially interest of guiding student learning mathematics, may advantageously facilitate carrying out of education activities.
Accompanying drawing explanation
With detailed description of the invention, this utility model is further illustrated below in conjunction with the accompanying drawings.
Fig. 1 is the front view of this utility model embodiment.
Fig. 2 is the structural representation after this utility model embodiment broken section.
Fig. 3 is the dorsal view of this utility model embodiment.
Label in figure:
1, instrument bezel support body, 2, rectangle interlayer, 3, fine sand, 4, grid, 5, scale.
Detailed description of the invention
As Figure 1-3, a kind of mathematics definite integral model, it is made up of instrument bezel support body 1, rectangle interlayer 2 and fine sand 3, instrument bezel support body 1 is made up of five clear glasses, and entirety is in top without the rectangular panel body shape of capping, and its internal gap is rectangle interlayer 2, rectangle interlayer 2 is relatively thin, rectangle interlayer 2 top is stretched out from the top of instrument bezel support body 1, leads to the external world, can put into fine sand 3 in rectangle interlayer 2；The back side at instrument bezel support body 1, the grid 4 of entire area it is carved with at corresponding rectangle interlayer 2, it is carved with horizontal scale 5 below instrument bezel support body 1 back side grid 4, being carved with longitudinal scale 5 on the right side of instrument bezel support body 1 back side grid 4, the unit scales of horizontal and vertical scale 5 aligns with the transverse and longitudinal line of grid 4.
During use, by mathematics definite integral model just facing to user, rectangle interlayer 2 is opening up, fine sand 3 is sprinkled in rectangle interlayer 2, form pattern as shown in Figure 2, because the thickness of rectangle interlayer 2 is the least, it is assumed that the curved surface that in rectangle interlayer 2, fine sand 3 is formed regards change parallel with baseplane as, and the area that in mathematics definite integral model front view 1, fine sand 3 presents is exactly the trapezoidal area of the curl expressed by definite integral.
Sand grains is the most tiny, it is assumed that ignore in the space between sand.
The character 1 of definite integral:
If in intervalOn, then .
Application: load a certain amount of fine sand 3 in mathematics definite integral model, give expression to the numerical value that trapezoidal area of curl is exactly a definite integral, the trapezoidal upper surface of curl if reinstalling a small amount of fine sand 3 in rectangle interlayer 2 and corresponding after ensureing to load new fine sand 3 be in before the top of curl trapezoidal upper surface.Make fine sand 3 amount in vessel many because newly enclosing fine sand 3, big before the area ratio that certain corresponding new curl is trapezoidal, say, that to understand guarantor's property of definite integral.
The character 2 of definite integral: setAndIt is function respectivelyIn intervalOn maximum and minima,
Then.
Application: after putting into fine sand 3 in mathematics definite integral model, fine sand 3 upper surface presents a curved surface, by scale 5 it may be seen that peak value corresponding to this curved surface and minimum point value, curl trapezoidal area corresponding in mathematics definite integral model is bound to more than the rectangular area corresponding to minimum point as height because in vessel fine sand 3 than this rectangle time sand many.In like manner, corresponding in mathematics definite integral model curl trapezoidal area is bound to less than the rectangular area corresponding to peak as height.
The character 3 of definite integral: if functionIn closed intervalUpper continuously then in integrating rangeOn at least there is a point, make .
Application: in mathematics definite integral model, fine sand 3 upper surface presents any one irregular curved surface, it is trapezoidal that one curl of expression faced by this mathematics definite integral model, corresponding curl trapezoidal faces product value.Make the fine sand 3 in rectangle interlayer 2 in a plane parallel with mathematics definite integral model bottom surface along with rocking mathematics definite integral model, the area that in this time mathematics definite integral model, fine sand 3 is expressed be exactly one with just now with the area of rectangle at the end, because the sand amount of fine sand 3 does not change in mathematics definite integral model, so demonstrating INTEGRAL THEOREM OF MEAN, it may be assumed that the continuous function at least existence on closed interval is a bitSo that ..Again because the curve that the upper surface in mathematics definite integral model faces correspondence must be full curve, the height of the rectangular area identical with former curl trapezoidal area must be between the maximum and minima of curve, and necessarily identical with the height of certain point on curve.INTEGRAL THEOREM OF MEAN must be demonstrate,proved.
Claims (1)
1. a mathematics definite integral model, it is characterized in that: it is made up of instrument bezel support body (1), rectangle interlayer (2) and fine sand (3), instrument bezel support body (1) is made up of five clear glasses, overall in top without the rectangular panel body shape of capping, its internal gap is rectangle interlayer (2), and rectangle interlayer (2) is relatively thin, and rectangle interlayer (2) top is stretched out from the top of instrument bezel support body (1), lead to the external world, fine sand (3) can be put in rectangle interlayer (2)；The back side in instrument bezel support body (1), the grid (4) of entire area is carved with at corresponding rectangle interlayer (2) place, it is carved with horizontal scale (5) in lower section, instrument bezel support body (1) back side grid (4), being carved with longitudinal scale (5) on right side, instrument bezel support body (1) back side grid (4), the unit scales of horizontal and vertical scale (5) aligns with the transverse and longitudinal line of grid (4).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201521095149.9U CN205451606U (en) | 2015-12-27 | 2015-12-27 | Mathematics definite integral model |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201521095149.9U CN205451606U (en) | 2015-12-27 | 2015-12-27 | Mathematics definite integral model |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN205451606U true CN205451606U (en) | 2016-08-10 |
Family
ID=56577830
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201521095149.9U Expired - Fee Related CN205451606U (en) | 2015-12-27 | 2015-12-27 | Mathematics definite integral model |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN205451606U (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113628508A (en) * | 2021-08-18 | 2021-11-09 | 临沂职业学院 | Display device and display method for mathematical integral area |
-
2015
- 2015-12-27 CN CN201521095149.9U patent/CN205451606U/en not_active Expired - Fee Related
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113628508A (en) * | 2021-08-18 | 2021-11-09 | 临沂职业学院 | Display device and display method for mathematical integral area |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20160810 Termination date: 20161227 |