Applied Mathematical Sciences

Partial Differential Equations I

Basic Theory

Authors: Taylor, Michael

  • Three volumes offer complete reference to PDEs
  • Includes both theory and applications
  • Lots of examples and exercises
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About this Textbook

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)

About the authors

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

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)


Table of contents (8 chapters)

  • Basic Theory of ODE and Vector Fields

    Taylor, Michael E.

    Pages 1-126

  • The Laplace Equation and Wave Equation

    Taylor, Michael E.

    Pages 127-195

  • Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE

    Taylor, Michael E.

    Pages 197-313

  • Sobolev Spaces

    Taylor, Michael E.

    Pages 315-352

  • Linear Elliptic Equations

    Taylor, Michael E.

    Pages 353-480

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4419-7055-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4419-7054-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4614-2726-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Partial Differential Equations I
Book Subtitle
Basic Theory
Authors
Series Title
Applied Mathematical Sciences
Series Volume
115
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-7055-8
DOI
10.1007/978-1-4419-7055-8
Hardcover ISBN
978-1-4419-7054-1
Softcover ISBN
978-1-4614-2726-1
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XXII, 654
Topics