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An Introduction to Partial Differential Equations

  • Michael Renardy
  • Robert C. Rogers

Part of the Texts in Applied Mathematics book series (TAM, volume 13)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Pages 1-35
  3. Pages 36-66
  4. Pages 101-121
  5. Pages 122-173
  6. Pages 174-202
  7. Pages 203-227
  8. Pages 228-282
  9. Pages 395-425
  10. Back Matter
    Pages 426-434

About this book

Introduction

 Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics.

This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in chapter 10, and the necessary tools from functional analysis are developed within the coarse. The book can be used to teach a variety of different courses.

This new edition features new problems throughout, and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.

Keywords

Algebra Sobolev space calculus mechanics modeling operator operator theory partial differential equation

Authors and affiliations

  • Michael Renardy
    • 1
  • Robert C. Rogers
    • 1
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97427
  • Copyright Information Springer-Verlag New York, Inc. 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-00444-0
  • Online ISBN 978-0-387-21687-4
  • Series Print ISSN 0939-2475
  • Buy this book on publisher's site