Synopses & Reviews
This book examines the complicated subject of Partial Differential Equations (PDEs). It involves the reader throughout by presenting theory, examples and exercises together. Both the classical and abstract aspects of the theory are dealt with, so that, for example, classical and generalised solutions in Sobolev and distribution spaces are treated. Most of the work is devoted to second or higher order PDEs; part of the distribution theory is included, covering Dirac's delta distribution delta function. Many practical tools are offered for solving important problems with the basic three PDEs, namely the wave equation, the Laplace equation, the heat equation and their generalisations. The majority of the problems are mathematical in character, though often physical interpretations are given. Audience: This volume is intended for undergraduate and graduate students in mathematics, physics technology and economics interested in PDEs for modelling complex systems.
Description
Includes bibliographical references (p. 397-399) and index.
Table of Contents
Preface. List of Symbols. 1. Introduction. 2. First Order PDEs. 3. Classification of the Second Order PDEs. 4. Hyperbolic Equations. 5. Elliptic Equations. 6. Parabolic Equations. 7. Numerical Methods. 8. Lebesgue's Integral, Fourier Transform. 9. Generalized Derivative and Sobolev Spaces. 10. Some Elements from Functional Analysis. 11. Functional Analysis Methods in PDEs. 12. Distributions in the Theory of PDEs. Bibliography. Index.