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Partial Differential Equations : Graduate Texts In Mathematics - Jeffrey Rauch

Partial Differential Equations

Graduate Texts In Mathematics

Hardcover Published: 9th January 1997
ISBN: 9780387974729
Number Of Pages: 266

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This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differen- tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the "essentials" can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.

"...this is an outstanding text presenting a healthy challenge not only to students but also to teachers used to more traditional or more pedestrian developments of the subject.--MATHEMATICAL REVIEWS

Power Series Methods
Some Harmonic Analysis
Solution of Initial Value Problems by Fourier Synthesis
Propagators and x-Space Methods
The Dirichlet Problem
Appendix: A Crash Course in Distribution Theory
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387974729
ISBN-10: 0387974725
Series: Graduate Texts In Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 266
Published: 9th January 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.13 x 16.51  x 1.91
Weight (kg): 0.57
Edition Number: 2