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Partial Differential Equations I

Basic Theory

  • Textbook
  • © 2011

Overview

Authors:
  1. Michael E. Taylor

    1. Department of Mathematics, University of North Carolina, Chapel Hill, USA

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  • Three volumes offer complete reference to PDE's
  • Includes both theory and applications
  • Lots of examples and exercises
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Basic Theory of ODE and Vector Fields

    • Michael E. Taylor
    Pages 1-126

  3. The Laplace Equation and Wave Equation

    • Michael E. Taylor
    Pages 127-195

  4. Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE

    • Michael E. Taylor
    Pages 197-313

  5. Sobolev Spaces

    • Michael E. Taylor
    Pages 315-352

  6. Linear Elliptic Equations

    • Michael E. Taylor
    Pages 353-480

  7. Linear Evolution Equations

    • Michael E. Taylor
    Pages 481-547

  8. Outline of Functional Analysis

    • Michael E. Taylor
    Pages 549-615

  9. Manifolds, Vector Bundles, and Lie Groups

    • Michael E. Taylor
    Pages 617-648

  10. Back Matter

    Pages 649-654
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Keywords

About this book

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.

Reviews

From the reviews:

“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)

From the reviews of the second edition:

“This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. … Graduate students … will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. … an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics.” (Christian Constanda, The Mathematical Association of America, June, 2011)

Authors and Affiliations

  • Department of Mathematics, University of North Carolina, Chapel Hill, USA

    Michael E. Taylor

About the author

Michael E. Taylor is a Professor at North Carolina University in the Department of Mathematics.

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