Partial Differential Equations ? Basic Theory - Softcover

Michael Eugene Taylor

Softcover

ISBN 10: 8181284143 ISBN 13: 9788181284143

Publisher: Springer, 2009

Synopsis

About the Book :- 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. Contents :- Series Preface Introduction 1.Basic Theory of ODE and Vector Fields 2.The Laplace Equation and Wave Equation 3.Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE 4.Sobolev Spaces 5.Linear Elliptic Equations 6.Linear Evolution Equations A.Outline of Functional Analysis B.Manifolds, Vector Bundles, and Lie Groups Index.

Edition details

• Publisher: Springer
• Publication date: 2009
• ISBN 10: 8181284143
• ISBN 13: 9788181284143
• Binding: Paperback
• Language: English
• Number of pages: 576