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 Please note that this resource requires at least version 1.5 of Java (JRE).
6 supplemental documents are available
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
Integral Approximations
Integral approximations of the sine function. download 1319kb .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 … download 1332kb .jar Last Modified: September 5, 2011
1 source code document is available
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
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Record Link
<a href="http://www.compadre.org/portal/items/detail.cfm?ID=11444">Roess, Dieter. "Calculus Models."</a>
AIP Format
D. Roess, Computer Program CALCULUS MODELS (2011), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11444&DocID=2408).
AJP/PRST-PER
D. Roess, Computer Program CALCULUS MODELS (2011), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11444&DocID=2408>.
APA Format
Roess, D. (2011). Calculus Models [Computer software]. Retrieved August 25, 2016, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11444&DocID=2408
Chicago Format
Roess, Dieter. "Calculus Models." http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11444&DocID=2408 (accessed 25 August 2016).
MLA Format
Roess, Dieter. Calculus Models. Computer software. 2011. Java (JRE) 1.5. 25 Aug. 2016 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11444&DocID=2408>.
BibTeX Export Format
@misc{
Author = "Dieter Roess",
Title = {Calculus Models},
Month = {September},
Year = {2011}
}
Refer Export Format
%A Dieter Roess
EndNote Export Format
%0 Computer Program Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
Citation Source Information
The AIP Style presented is based on information from the AIP Style Manual. The APA Style presented is based on information from APA Style.org: Electronic References. The Chicago Style presented is based on information from Examples of Chicago-Style Documentation. The MLA Style presented is based on information from the MLA FAQ. Calculus Models:
Is Based On
Easy Java Simulations Modeling and Authoring Tool
The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Calculus Models. relation by Wolfgang ChristianKnow of another related resource? Login to relate this resource to it. |
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