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A Library Of Matlab Scripts For Illustration And Animation Of Solutions To Partial Differential Equations

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Conference

2007 Annual Conference & Exposition

Location

Honolulu, Hawaii

Publication Date

June 24, 2007

Start Date

June 24, 2007

End Date

June 27, 2007

ISSN

2153-5965

Conference Session

Computed Simulation and Animation

Tagged Division

Computers in Education

Page Count

13

Page Numbers

12.58.1 - 12.58.13

Permanent URL

https://peer.asee.org/1703

Download Count

172

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Paper Authors

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Raymond Jacquot University of Wyoming

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Ray Jacquot, Ph.D., P.E., received his BSME and MSME degrees at the University of Wyoming in 1960 and 1962 respectively. He was an NSF Science Faculty Fellow at Purdue University where he received the Ph.D. in 1969. He joined the Electrical Engineering faculty of the University of Wyoming in 1969. He is a member of ASEE, IEEE and ASME and has been active in ASEE for over three decades serving as Rocky Mountain Section Chair and PIC IV Chair. His professional interests are in modeling, control and simulation of dynamic systems. He is currently Professor Emeritus of Electrical and Computer Engineering. E-mail: quot@uwyo.edu.

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Cameron Wright University of Wyoming Orcid 16x16 orcid.org/0000-0002-6029-1896

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Cameron H. G. Wright, Ph.D, P.E., is on the faculty of the Department of Electrical and Computer Engineering at the University of Wyoming, Laramie, WY. He was previously Professor and Deputy Department Head of the Electrical Engineering Department at the U.S. Air Force Academy. His research interests include signal and image processing, biomedical instrumentation, communications systems, and laser/electro-optics applications. Dr. Wright is a member of ASEE, IEEE, SPIE, NSPE, Tau Beta Pi, and Eta Kappa Nu. E-mail: c.h.g.wright@ieee.org.

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Robert Kubichek University of Wyoming

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Robert F. Kubichek received his Ph.D. from the University of Wyoming in 1985. He has worked in research positions at the BDM Corporation and the Institute for Telecommunication Sciences (U.S. Dept. of Commerce), and was an adjunct professor at the University of Colorado from 1989-1991. He joined the University of Wyoming in 1991, where he is currently an Associate Professor. Current research interests include speech analysis for intelligibility and speech quality, and developing new diagnostic tools for speech disorders. E-mail: kubichek@uwyo.edu.

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Thomas Edgar University of Wyoming

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Thomas Edgar received the Ph.D. from Colorado State University in 1983. He teaches geotechnical engineering and groundwater hydrology courses in the Department of Civil and Architectural Engineering at the University of Wyoming. He is an Associate Professor and has been an award winning teacher in University and the Department. He is currently the coordinator for the freshman orientation classes in the college. E-mail tvedgar@uwyo.edu.

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Abstract
NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

A Library of MATLABTM Scripts for Illustration and Animation of Solutions to Partial Differential Equations

Introduction

In the past three years the authors have developed a series of MATLABTM scripts that illustrate the solutions to partial differential equations commonly encountered in mathematics, engineering and physics courses. The objective of this paper is to create awareness, among teaching faculty, of the availability of this set of MATLABTM scripts to aid their teaching of physical phenomena governed by partial differential equations.

Over many years the authors have observed the difficulty students have with the solutions to partial differential equation problems and when they have completed such a solution they still cannot associate a physical interpretation with the resulting equation or equations. Since many students are graphical learners, we asked ourselves how the high quality and easy to use graphics available in MATLABTM might be exploited to help students better understand the solutions that they, their instructor or the textbook may have generated.

There has been considerable work done to exploit the use of computer graphics to clarify physical problems governed by partial differential equations. An early paper used MATLABTM to illustrate solutions to hyperbolic differential equations.1 Several papers at about the same time used computer animation to illustrate solutions for elastic wave propagation and beam vibration.2,3 The concept of using MATLABTM for the animation of lumped parameter dynamic systems was demonstrated by Watkins et al.4 Recently there have been a number of papers describing the graphical interpretation of partial differential equations. The transport of pollutants in groundwater has been described using web-based graphics5 and another paper reports a virtual laboratory for teaching quasistationary electromagnetics.6 Another recent paper discusses the solution of groundwater problems using a spreadsheet.7 Still another paper employs a spreadsheet to examine the topic of electromagnetic wave propagation.8 Two recent papers reported the use of animation to clarify a variety of partial differential equation solutions.9,10 There are a number of approaches to the animation of distributed parameter systems and one is the application of finite element software (ANSYSTM) to illustrate the vibration of beams and plates.11 A recent paper discusses the use of animation in MATLABTM to animate the solution to a variety of electrical transmission line problems.12 A very recent paper discusses how MATLABTM has been employed to illustrate the downwind transport of the chemical components of industrial stack emissions.13

Strategies for PDE Solution Presentation

There are a number of possible ways that graphical presentations may be employed to clarify responses of dynamic systems described by partial differential equations with one spatial variable and time as independent variables. The most obvious are:

• A plot of the solution as a function of time for several locations (location as a parameter). • A plot of the solution as a function of the spatial variable for several values of time (time as a parameter).

Jacquot, R., & Wright, C., & Kubichek, R., & Edgar, T. (2007, June), A Library Of Matlab Scripts For Illustration And Animation Of Solutions To Partial Differential Equations Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. https://peer.asee.org/1703

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