Overview
- Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations
- Includes a large number of exercises and solutions expanding on themes developed in the main text
- Clear explanations, motivations, and illustration of all necessary mathematical concepts
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (7 chapters)
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Front Matter
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Potentials, Diffusions, and Waves
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Front Matter
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Nonlinear Partial Differential Equations
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Front Matter
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Back Matter
Keywords
About this book
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis.
Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger’s equations, KdV equations, and the equations of gas dynamics and porous media are also covered.
The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.
Features
· Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum.
· Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book.
· Clear explanations, motivations, and illustration of all necessary mathematical concepts.
Reviews
From the reviews:
“The book will be useful to graduate students and researchers who are interested in the applications of distributions and partial differential equations to the applied sciences.” (Denise Huet, zbMATH, Vol. 1283, 2014)
Authors and Affiliations
Bibliographic Information
Book Title: Distributions in the Physical and Engineering Sciences, Volume 2
Book Subtitle: Linear and Nonlinear Dynamics in Continuous Media
Authors: Alexander I. Saichev, Wojbor A. Woyczynski
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-0-8176-4652-3
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-0-8176-3942-6Published: 05 September 2013
Softcover ISBN: 978-1-4939-5020-1Published: 24 September 2016
eBook ISBN: 978-0-8176-4652-3Published: 05 September 2013
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XXIV, 409
Number of Illustrations: 126 b/w illustrations, 18 illustrations in colour
Topics: Mathematics, general