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 – Plus 2000 Examples from Physics" ISBN 978-3-11-025005-3, Walter de Gruyter GmbH & Co. KG

Please note that this resource requires
at least version 1.5 of
Java (JRE).

Difference And Differential Quotient Model
The transition from the difference quotient to the differential quotient (first derivative) is demonstrated for the sine function. download 1318kb .jar
Last Modified: September 5, 2011

First and Second Derivative Model
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 .jar
Last Modified: September 5, 2011

Definite Integral
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 .jar
Last Modified: September 5, 2011

Riemann and Lebesgue Integral Model
The simulation uses a parabola to demonstrate the Riemann integral and the Lebesgue integral. download 1333kb .jar
Last Modified: September 5, 2011

Riemann Integral Model 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 …
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.

Calculus Models Source Code
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 .zip
Last Modified: September 5, 2011

Roess, D. (2011). Calculus Models [Computer software]. Retrieved February 23, 2017, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11444&DocID=2408

%0 Computer Program %A Roess, Dieter %D September 5, 2011 %T Calculus Models %8 September 5, 2011 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11444&DocID=2408

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