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Partial Differential Equations I

Basic Theory

  • Textbook
  • © 2023
  • Latest edition

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

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxiv
    Download chapter PDF

  2. Basic Theory of ODE and Vector Fields

    • Michael E. Taylor
    Pages 1-136

  3. The Laplace Equation and Wave Equation

    • Michael E. Taylor
    Pages 137-205

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

    • Michael E. Taylor
    Pages 207-336

  5. Sobolev Spaces

    • Michael E. Taylor
    Pages 337-374

  6. Linear Elliptic Equations

    • Michael E. Taylor
    Pages 375-515

  7. Linear Evolution Equations

    • Michael E. Taylor
    Pages 517-592

  8. Back Matter

    Pages 593-714
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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.

The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters.  In includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids.  The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds.

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.”

(Peter Lax, SIAM review, June 1998)


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.

Bibliographic Information

  • Book Title: Partial Differential Equations I

  • Book Subtitle: Basic Theory

  • Authors: Michael E. Taylor

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-031-33859-5

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-33858-8Published: 07 December 2023

  • Softcover ISBN: 978-3-031-33861-8Due: 07 January 2024

  • eBook ISBN: 978-3-031-33859-5Published: 06 December 2023

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 3

  • Number of Pages: XXIV, 714

  • Number of Illustrations: 40 b/w illustrations

  • Topics: Partial Differential Equations, Manifolds and Cell Complexes (incl. Diff.Topology)

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