Applied and Numerical Harmonic Analysis

Distributions in the Physical and Engineering Sciences, Volume 2

Linear and Nonlinear Dynamics in Continuous Media

Authors: Saichev, Alexander I., Woyczynski, Wojbor

  • 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
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  • ISBN 978-0-8176-4652-3
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  • ISBN 978-0-8176-3942-6
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About this Textbook

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)


Table of contents (7 chapters)

  • Potential Theory and Fundamental Solutions of Elliptic Equations

    Saichev, Alexander I. (et al.)

    Pages 3-57

  • Diffusions and Parabolic Evolution Equations

    Saichev, Alexander I. (et al.)

    Pages 59-91

  • Waves and Hyperbolic Equations

    Saichev, Alexander I. (et al.)

    Pages 93-142

  • First-Order Nonlinear PDEs and Conservation Laws

    Saichev, Alexander I. (et al.)

    Pages 145-170

  • Generalized Solutions of First-Order Nonlinear PDEs

    Saichev, Alexander I. (et al.)

    Pages 171-227

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-4652-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-0-8176-3942-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4939-5020-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Distributions in the Physical and Engineering Sciences, Volume 2
Book Subtitle
Linear and Nonlinear Dynamics in Continuous Media
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-4652-3
DOI
10.1007/978-0-8176-4652-3
Hardcover ISBN
978-0-8176-3942-6
Softcover ISBN
978-1-4939-5020-1
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XXIV, 409
Number of Illustrations and Tables
126 b/w illustrations, 18 illustrations in colour
Topics