Analytical Techniques for Solving Nonlinear Partial Differential Equations (Synthesis Lectures on Mathematics and Statistics)

167 Pages·2019·1.143 MB·English

by  Steven G. Krantz (editor), Daniel J. Arrigo

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Series ISSN: 1938-1743 A
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Series Editor: Steven G. Krantz, Washington University in St. Louis A
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Analytical Techniques for Solving Nonlinear A
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Partial Differential Equations C
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Daniel J. Arrigo, University of Central Arkansas U
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This is an introduction to methods for solving nonlinear partial differential equations
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(NLPDEs). After the introduction of several PDEs drawn from science and engineering, O
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the reader is introduced to techniques used to obtain exact solutions of NPDEs. The chapters V
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include the following topics: Compatibility, Differential Substitutions, Point and Contact G
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Transformations, First Integrals, and Functional Separability. The reader is guided through O
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these chapters and is provided with several detailed examples. Each chapter ends with a series L
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of exercises illustrating the material presented in each chapter. E
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The book can be used as a textbook for a second course in PDEs (typically found R
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in both science and engineering programs) and has been used at the University of Central R
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Arkansas for more than ten years. IA
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About SYNTHESIS
This volume is a printed version of a work that appears in the Synthesis
Digital Library of Engineering and Computer Science. Synthesis
books provide concise, original presentations of important research and M
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development topics, published quickly, in digital and print formats. R
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Analytical Techniques for
Solving Nonlinear Partial
Differential Equations

Synthesis Lectures on
Mathematics and Statistics
Editor
StevenG.Krantz,WashingtonUniversity,St.Louis
AnalyticalTechniquesforSolvingNonlinearPartialDifferentialEquations
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2019
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Copyright©2019byMorgan&Claypool
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin
anyformorbyanymeans—electronic,mechanical,photocopy,recording,oranyotherexceptforbriefquotations
inprintedreviews,withoutthepriorpermissionofthepublisher.
AnalyticalTechniquesforSolvingNonlinearPartialDifferentialEquations
DanielJ.Arrigo
www.morganclaypool.com
ISBN:9781681735337 paperback
ISBN:9781681735344 ebook
ISBN:9781681735351 hardcover
DOI10.2200/S00907ED1V01Y201903MAS025
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONMATHEMATICSANDSTATISTICS
Lecture#25
SeriesEditor:StevenG.Krantz,WashingtonUniversity,St.Louis
SeriesISSN
Print1938-1743 Electronic1938-1751
Analytical Techniques for
Solving Nonlinear Partial
Differential Equations
Daniel J. Arrigo
UniversityofCentralArkansas
SYNTHESISLECTURESONMATHEMATICSANDSTATISTICS#25
M
&C Morgan &cLaypool publishers
ABSTRACT
This is an introduction to methods for solving nonlinear partial differential equations
(NLPDEs). After the introduction of several PDEs drawn from science and engineering, the
readerisintroducedtotechniquesusedtoobtainexactsolutionsofNPDEs.Thechaptersinclude
thefollowingtopics:Compatibility,DifferentialSubstitutions,PointandContactTransforma-
tions, First Integrals, and Functional Separability. The reader is guided through these chapters
and is provided with several detailed examples. Each chapter ends with a series of exercises
illustratingthematerialpresentedineachchapter.
ThebookcanbeusedasatextbookforasecondcourseinPDEs(typicallyfoundinboth
scienceandengineeringprograms)andhasbeenusedattheUniversityofCentralArkansasfor
morethantenyears.
KEYWORDS
nonlinear partial differential equations, compatibility, differential substitutions,
pointandcontacttransformations,firstintegrals,functionalseparability