APS Excellence in Physics Education Award
November 2019
Science SPORE Prize
November 2011
The Open Source Physics Project is supported by NSF DUE-0442581.
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Calculus Models Documents
This material has 8 associated documents. Select a document title to view a document's information.
Main Document
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
Last Modified May 29, 2013
 This file has previous versions.
Supplemental Documents (6)
The transition from the difference quotient to the differential quotient (first derivative) is demonstrated for the sine function.
Last Modified September 5, 2011
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 of the sine function.
Last Modified September 5, 2011
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
The simulation uses a parabola to demonstrate the Riemann integral and the Lebesgue integral.
Last Modified September 5, 2011
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
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
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Calculus Models
