Partial Differential Equations 1: Foundations and Integral Representations

✍ Scribed by Friedrich Sauvigny

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 456
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

This comprehensive two-volume textbook covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is placed on the connection of PDEs and complex variable methods. In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations. We solve partial differential equations via integral representations in this volume, reserving functional analytic solution methods for Volume Two.

✦ Table of Contents

Cover......Page 1
Universitext......Page 2
Partial Differential
Equations 1......Page 4
ISBN-13 9783540344575......Page 5
Introduction to Volume 1 – Foundations and
Integral Representations......Page 8
Contents of Volume 1
Foundations and Integral Repesentations......Page 12
Contents of Volume 2 Functional Analytic
Methods......Page 14
I
Differentiation and Integration on Manifolds......Page 16
II
Foundations of Functional Analysis......Page 106
III
Brouwer’s Degree of Mapping with Geometric
Applications......Page 190
IV
Generalized Analytic Functions......Page 230
V
Potential Theory and Spherical Harmonics......Page 312
VI
Linear Partial Differential Equations in Rn......Page 370
References......Page 446
Index......Page 448
Universitext......Page 453