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＜電子ブック＞
Partial Differential Equations 1 : Foundations and Integral Representations / by Friedrich Sauvigny
(Universitext. ISSN:21916675)

版	2nd ed. 2012.
出版者	(London : Springer London : Imprint: Springer)
出版年	2012
大きさ	XV, 447 p. 16 illus : online resource
著者標目	*Sauvigny, Friedrich author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics FREE:Differential Equations FREE:Mathematical Methods in Physics
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4471-2981-3

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