Partial Differential Equations 1
Foundations and Integral Representations
Authors: Sauvigny, Friedrich
Free Preview- 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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- About this Textbook
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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
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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)
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Differentiation and Integration on Manifolds
Pages 1-90
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Foundations of Functional Analysis
Pages 91-173
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Brouwer’s Degree of Mapping
Pages 175-214
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Generalized Analytic Functions
Pages 215-304
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Potential Theory and Spherical Harmonics
Pages 305-361
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Table of contents (6 chapters)
- Download Preface 1 PDF (173.3 KB)
- Download Sample pages 2 PDF (1 MB)
- Download Table of contents PDF (162.1 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Partial Differential Equations 1
- Book Subtitle
- Foundations and Integral Representations
- Authors
-
- Friedrich Sauvigny
- 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
- 16 b/w illustrations
- Topics
