Universitext

Partial Differential Equations 1

Foundations and Integral Representations

Authors: Sauvigny, Friedrich

  • Provides a complete and thorough introduction into the theory of linear and nonlinear partial differential equations
  • Presents interesting applications to physics and differential geometry
  • Includes the basic methods from linear and nonlinear functional analysis
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eBook $59.99
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  • ISBN 978-1-4471-2981-3
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-1-4471-2980-6
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  • Usually dispatched within 3 to 5 business days.
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About this Textbook

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.

In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated:

• integration and differentiation on manifolds

• foundations of functional analysis

• Brouwer's mapping degree

• generalized analytic functions

• potential theory and spherical harmonics

• linear partial differential equations

This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added.

The second volume will present functional analytic methods and applications to problems in differential geometry.

This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study.

Reviews

From the reviews of the second edition:

“The revised and enlarged version of this volume gives a special emphasis to geometric and complex variable methods involving integral representations. The new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added. … This unique book will become a standard reference and it should be found in every mathematical library.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1246, 2012)


Table of contents (6 chapters)

  • Differentiation and Integration on Manifolds

    Sauvigny, Friedrich

    Pages 1-90

  • Foundations of Functional Analysis

    Sauvigny, Friedrich

    Pages 91-173

  • Brouwer’s Degree of Mapping

    Sauvigny, Friedrich

    Pages 175-214

  • Generalized Analytic Functions

    Sauvigny, Friedrich

    Pages 215-304

  • Potential Theory and Spherical Harmonics

    Sauvigny, Friedrich

    Pages 305-361

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4471-2981-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-1-4471-2980-6
  • 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 1
Book Subtitle
Foundations and Integral Representations
Authors
Series Title
Universitext
Copyright
2012
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-2981-3
DOI
10.1007/978-1-4471-2981-3
Softcover ISBN
978-1-4471-2980-6
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XV, 447
Number of Illustrations and Tables
16 b/w illustrations
Topics