APS Excellence in Physics Education Award
November 2019 Science SPORE Prize
November 2011 The Open Source Physics Project is supported by NSF DUE-0442581.

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

##### 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.

##### Integral Approximations

Integral approximations of the sine function.

##### 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.

##### Riemann and Lebesgue Integral Model

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

##### 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.

#### 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. Open Source Physics - EJS Modeling Tracker Physlet Physics Physlet Quantum Physics STP Book