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Partial Differential Equations

  • Jeffrey Rauch

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

Table of contents

  1. Front Matter
    Pages i-x
  2. Jeffrey Rauch
    Pages 1-60
  3. Jeffrey Rauch
    Pages 61-94
  4. Jeffrey Rauch
    Pages 137-171
  5. Jeffrey Rauch
    Pages 172-246
  6. Back Matter
    Pages 247-266

About this book

Introduction

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.

Keywords

Boundary value problem Derivative Differential operator Sobolev space calculus differential equation functional analysis maximum maximum principle ordinary differential equation partial differential equation wave equation

Authors and affiliations

  • Jeffrey Rauch
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0953-9
  • Copyright Information Springer-Verlag New York, Inc. 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6959-5
  • Online ISBN 978-1-4612-0953-9
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site