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Partial Differential Equations

  • Textbook
  • © 1991

Overview

Authors:
  1. Jeffrey Rauch

    1. Department of Mathematics, University of Michigan, Ann Arbor, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 128)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
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  2. Power Series Methods

    • Jeffrey Rauch
    Pages 1-60

  3. Some Harmonic Analysis

    • Jeffrey Rauch
    Pages 61-94

  4. Solution of Initial Value Problems by Fourier Synthesis

    • Jeffrey Rauch
    Pages 95-136

  5. Propagators and x-Space Methods

    • Jeffrey Rauch
    Pages 137-171

  6. The Dirichlet Problem

    • Jeffrey Rauch
    Pages 172-246

  7. Back Matter

    Pages 247-266
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Keywords

About this book

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.

Reviews

"...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

Authors and Affiliations

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Jeffrey Rauch

Bibliographic Information

  • Book Title: Partial Differential Equations

  • Authors: Jeffrey Rauch

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0953-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Hardcover ISBN: 978-0-387-97472-9Published: 23 December 1991

  • Softcover ISBN: 978-1-4612-6959-5Published: 17 October 2012

  • eBook ISBN: 978-1-4612-0953-9Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: X, 266

  • Topics: Analysis

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