Partial Differential Equations I

Basic Theory

  • Michael E. Taylor

Part of the Applied Mathematical Sciences book series (AMS, volume 115)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Michael E. Taylor
    Pages 1-126
  3. Michael E. Taylor
    Pages 127-195
  4. Michael E. Taylor
    Pages 315-352
  5. Michael E. Taylor
    Pages 353-480
  6. Michael E. Taylor
    Pages 481-547
  7. Michael E. Taylor
    Pages 549-615
  8. Michael E. Taylor
    Pages 617-648
  9. Back Matter
    Pages 649-654

About this book

Introduction

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, the space of pseudodifferential operators of harmonic oscillator type, and an index formula for elliptic systems of such operators. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time.

Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC.

Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”

(SIAM Review, June 1998)

Keywords

Basic Theory of ODE and Vector Fields Fourier Analysis Laplace Equation Linear Elliptic Equations Wave Equation

Authors and affiliations

  • Michael E. Taylor
    • 1
  1. 1., Department of MathematicsUniversity of North CarolinaChapel HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7055-8
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7054-1
  • Online ISBN 978-1-4419-7055-8
  • Series Print ISSN 0066-5452
  • About this book