Partial Differential Equations.Vol.1

The first of two volumes that comprehensively treat partial differential equations, this revised second edition focuses on geometric and complex variable methods involving integral representations. Topics such as Brouwer's mapping degree are treated in detail.

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.

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 Includes supplementary material: sn.pub/extras

Autorentext

Friedrich Sauvigny studierte Mathematik mit Physik im Anwendungsfach an der Universität Göttingen, wo er anschließend auch promovierte und sich habilitierte. Währenddessen war er als wissenschaftlicher Assistent an der RWTH Aachen, als akademischer Rat an der TU Clausthal sowie als Gastwissenschaftler an der Universität Bonn tätig. Im Anschluss wurde er zunächst Assistant Professor an der University of Wisconsin-Milwaukee und dann Professor an der BTU Cottbus-Senftenberg, wo er sich nun im Ruhestand befindet. Sein Arbeitsgebiet bilden die partiellen Differentialgleichungen und die geometrische Analysis.

Inhalt

Differentiation and Integration on Manifolds.- Foundations of Functional Analysis.- Brouwer's Degree of Mapping.- Generalized Analytic Functions.- Potential Theory and Spherical Harmonics.- Linear Partial Differential Equations in **** R ** n ** .