Partial Differential Equations: Volumes 1 & 2

This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put 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. While we solve the partial differential equations via integral representations in this volume, we shall present functional analytic solution methods in the second volume.

This textbook can be chosen for a course over several semesters on a medium level. Advanced readers may study each chapter independently from the others.

Table of contents - Volume 1

- Differentiation and Integration on Manifolds.
- Foudations of Functional Analysis.
- Brouwer´s Degree of Mapping with Geometric Applications.
- Generalized Analytic Functions.
- Potential Theory and Spherical Harmonics.
- Linear Partial Differential Equations in Rn.


Table of contents - Volume 2

- Operators in Banach Spaces.
- Linear Operators in Hilbert Spaces.
- Linear Elliptic Differential Equations.
- Weak Solutions of Elliptic Differential Equations.
- Nonlinear Partial Differential Equations.
- Nonlinear Elliptic Systems.