文档介绍：o9 FEV. 1988
SCHAUM'S OUTLINE OF
THEORY AND PROBLEMS
of
PARTIAL
DIFFERENTIAL
EQUATIONS
•
PAUL DUCHATEAU, .
DAVID W. ZACHMANN, .
Professors of Mathematics
Colorado State University
•
SCHAUM'S OUTLINE SERIES
McGRAW-HILL PANY
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Preface
The importance of partial differential equations among the topics of applied
mathematics bas been recognized for many years. However, the increasing
complexity of today's technology is demanding of the mathematician, the engineer,
and the scientist an understanding of the subject previously attained only by
specialists. This book is intended to serve as a supplemental or primary text for a
course aimed at providing this understanding. It has anized so as to
provide a helpful reference for the practicing professional, as well.
After the introductory Chapter 1, the book is divided into three parts. Part I,
consisting of Chapters 2 through 5, is devoted primarily to qualitative aspects of the
subject. Chapter 2 discusses the classification of problems, while Chapters 3 and 4
characterize the behavior of solutions to elliptic boundary value problems and
evolution equations, respectively. Chapter 5 focuses on hyperbolic systems of
equations of order one.
Part prises Chapters 6 through 8, which present the principal tech•
niques for constructing exact solutions to linear problems in partial differential
equations. Chapter 6 contains the essential ideas of eigenfunction expansions and
integral transforms, which are then applied to partial differential equations in
Chapter 7. Chapter 8 provides a practical treatment of the important topic of
Green's functions and fundamental solutions.
Part III, Chapters 9 through 14, deals with the construction of approxima