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Analytical Methods for Solving Nonlinear Partial Differential Equations
Buch von Daniel Arrigo
Sprache: Englisch

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Beschreibung
This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.
This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.
Über den Autor
Daniel Arrigo earned his PhD from the Georgia Institute of Technology in 1991. He has been on staff in the Department of Mathematics at the University of Central Arkansas since 1999 and is currently Professor of Mathematics. He has published over 30 journal articles and three books. His research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity. In 2008, Dr. Arrigo received the Oklahoma-Arkansas Section of the Mathematical Association of America's Award for Distinguished Teaching of College or University Mathematics and in 2019 the University of Central Arkansas's Teaching Excellence Award.
Zusammenfassung

Presents analytical methods to solve nonlinear partial differential equations (NLPDEs)

Includes techniques for solving first and second order NLPDEs and provides interdisciplinary examples

Contains numerous exercises throughout to facilitate learning and has been class tested over the past 10 years

Inhaltsverzeichnis
Nonlinear PDEs are Everywhere.- Differential Substitutions.- Point and Contact Transformations.- First Integrals.- Functional Separability.
Details
Erscheinungsjahr: 2022
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xii
174 S.
1 s/w Illustr.
2 farbige Illustr.
174 p. 3 illus.
2 illus. in color.
ISBN-13: 9783031170683
ISBN-10: 3031170687
Sprache: Englisch
Einband: Gebunden
Autor: Arrigo, Daniel
Auflage: Second Edition 2022
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 246 x 173 x 16 mm
Von/Mit: Daniel Arrigo
Erscheinungsdatum: 29.10.2022
Gewicht: 0,502 kg
Artikel-ID: 123329444
Über den Autor
Daniel Arrigo earned his PhD from the Georgia Institute of Technology in 1991. He has been on staff in the Department of Mathematics at the University of Central Arkansas since 1999 and is currently Professor of Mathematics. He has published over 30 journal articles and three books. His research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity. In 2008, Dr. Arrigo received the Oklahoma-Arkansas Section of the Mathematical Association of America's Award for Distinguished Teaching of College or University Mathematics and in 2019 the University of Central Arkansas's Teaching Excellence Award.
Zusammenfassung

Presents analytical methods to solve nonlinear partial differential equations (NLPDEs)

Includes techniques for solving first and second order NLPDEs and provides interdisciplinary examples

Contains numerous exercises throughout to facilitate learning and has been class tested over the past 10 years

Inhaltsverzeichnis
Nonlinear PDEs are Everywhere.- Differential Substitutions.- Point and Contact Transformations.- First Integrals.- Functional Separability.
Details
Erscheinungsjahr: 2022
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xii
174 S.
1 s/w Illustr.
2 farbige Illustr.
174 p. 3 illus.
2 illus. in color.
ISBN-13: 9783031170683
ISBN-10: 3031170687
Sprache: Englisch
Einband: Gebunden
Autor: Arrigo, Daniel
Auflage: Second Edition 2022
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 246 x 173 x 16 mm
Von/Mit: Daniel Arrigo
Erscheinungsdatum: 29.10.2022
Gewicht: 0,502 kg
Artikel-ID: 123329444
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