Partial Differential Equations 1: Foundations and Integral Representations

ISBN-13: 9781447129806 / Angielski / Miękka / 2012 / 447 str.

Friedrich Sauvigny

Opis

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.

Recenzje

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." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1246, 2012)

Spis treści

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 Rⁿ.