This material has **8** associated documents. Select a document title to view a document's information.

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written by
Dieter Roess
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The seven calculus models in this item demonstrate differentiation and integration of functions. The default Derivative Machine Model allows users to select a function and plot that function and its derivatives. Additional models are available as supplemental documents.

Calculus Models are part of "Learning and Teaching Mathematics using Simulations â€“ Plus 2000 Examples from Physics" ISBN 978-3-11-025005-3, Walter de Gruyter GmbH & Co. KG

**Download**- 1877kb Java Archive File*ejs_e_Derivatives.jar*

Last Modified *May 29, 2013*

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This file has previous versions.
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The transition from the difference quotient to the differential quotient (first derivative) is demonstrated for the sine function.

**Download**- 1318kb Java Archive File*ejs_e_Diff_limit_1.jar*

Last Modified *September 5, 2011*

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This simulation demonstrates the limit process in deriving the first derivative of a sine function with a superimposed linear term (a straight line) . For this case the second derivative should be independent of the linear term.

**Download**- 1330kb Java Archive File*ejs_e_Diff_limit_2.jar*

Last Modified *September 5, 2011*

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Integral approximations of the sine function.

**Download**- 1319kb Java Archive File*ejs_e_Integral_approximations.jar*

Last Modified *September 5, 2011*

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This simulation demonstrates definite integration of the sine function by the simple algorithm of summing approximative rectangles. The red curve shows the sine function itself.

**Download**- 1327kb Java Archive File*ejs_e_Integral_limit.jar*

Last Modified *September 5, 2011*

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The simulation uses a parabola to demonstrate the Riemann integral and the Lebesgue integral.

**Download**- 1333kb Java Archive File*ejs_e_Lebesgue_integral.jar*

Last Modified *September 5, 2011*

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An approximate Riemann Integral of a sine function is shown. The left window shows in red the approximation by the supinum series, with the blue point as the sum; the function always lies below the rectangle. The right window shows the approximation by the infimum series; the function always lies above the rectangle.

**Download**- 1332kb Java Archive File*ejs_e_Riemann_integral.jar*

Last Modified *September 5, 2011*

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The source code zip archive contains an EJS-XML representation of the Calculus models. Unzip this archive in your EJS workspace to compile and run this model using EJS.

**Download**- 31kb Compressed File*ejs_roess_Calculus.zip*

Last Modified *September 5, 2011*

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