Invitation to partial differential equations
著者
書誌事項
Invitation to partial differential equations
（Graduate studies in mathematics, 205）
American Mathematical Society, c2020
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注記
Includes bibliographical references (p. 311-313) and index
内容説明・目次
内容説明
This book is based on notes from a beginning graduate course on partial differential equations. Prerequisites for using the book are a solid undergraduate course in real analysis. There are more than 100 exercises in the book. Some of them are just exercises, whereas others, even though they may require new ideas to solve them, provide additional important information about the subject.
It is a great pleasure to see this book - written by a great master of the subject - finally in print. This treatment of a core part of mathematics and its applications offers the student both a solid foundation in basic calculations techniques in the subject, as well as a basic introduction to the more general machinery, e.g., distributions, Sobolev spaces, etc., which are such a key part of any modern treatment. As such this book is ideal for more advanced undergraduates as well as mathematically inclined students from engineering or the natural sciences.
目次
Linear differential operators
One-dimensional wave equation
The Sturm-Liouville problem
Distributions
Convolution and Fourier transform
Harmonic functions
The heat equation
Sobolev spaces. A generalized solution of Dirichlet's problem
The eigenvalues and eigenfunctions of the Laplace operator
The wave equation
Properties of the potentials and their computation
Wave fronts and short-wave asymptotics for hyperbolic equations
Answers and hints. Solutions
Bibliography
Index.
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