基本信息出版社：Springer
页码：437 页
出版日期：2006年09月
ISBN：3540344578
International Standard Book Number：3540344578
条形码：9783540344575
EAN：9783540344575
版本：1
装帧：平装
正文语种：英语
丛书名：Universitext
分册名：1

内容简介 在线阅读本书

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.

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From the reviews:

"Friedrich Sauvigny’s remarkable two-volume opus … constitutes the author’s attempt to treat the beautiful and difficult subject of PDEs in a thorough and instructive way … . is a fine place to learn PDEs with the goal of doing serious work in the field. … Friedrich Sauvigny’s scholarship is exemplary and thorough; at the same time his book is both broad and deep and is a pleasure to read." (Michael Berg, MathDL, February, 2007)

目录
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.
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