## Calculus Models Documents

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

#### 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 DifferentialÂ  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