Calculus Models Documents

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Main Document

Calculus Models 

written by Dieter Roess

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

Last Modified May 29, 2013

This file has previous versions.

Supplemental Documents (6)

Difference And Differential  Quotient Model 

The transition from the difference quotient to the differential quotient (first derivative) is demonstrated for the sine function.

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.

Last Modified September 5, 2011

Integral Approximations 

Integral approximations of the sine function.

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.

Last Modified September 5, 2011

Riemann and Lebesgue Integral Model 

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

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 series; the function always lies above the rectangle.

Last Modified September 5, 2011

Source Code Documents

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.

Last Modified September 5, 2011