Partial Differential Equations Basic Theory

ISBN-10: 0387946543

ISBN-13: 9780387946542

Edition: 1996

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Description:

This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
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Book details

List price: $99.00
Copyright year: 1996
Publisher: Springer
Publication date: 8/5/1999
Binding: Paperback
Pages: 588
Size: 6.50" wide x 9.25" long x 1.25" tall
Weight: 1.848
Language: English

Series Preface
Introduction
Basic Theory of ODE and Vector Fields
The Laplace Equation and Wave Equation
Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE
Sobolev Spaces
Linear Elliptic Equations
Linear Evolution Equations
App. A Outline of Functional Analysis
App. B Manifolds, Vector Bundles, and Lie Groups
Index
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