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＜電子ブック＞
An Introduction to Partial Differential Equations / by Michael Renardy, Robert C. Rogers
(Texts in Applied Mathematics. ISSN:21969949 ; 13)

版	2nd ed. 2004.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2004
本文言語	英語
大きさ	XIV, 434 p. 21 illus : online resource
著者標目	*Renardy, Michael author Rogers, Robert C author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematics LCSH:Mathematical physics LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Differential Equations FREE:Applications of Mathematics FREE:Mathematical Methods in Physics FREE:Mathematical and Computational Engineering Applications
一般注記	Characteristics -- Conservation Laws and Shocks -- Maximum Principles -- Distributions -- Function Spaces -- Sobolev Spaces -- Operator Theory -- Linear Elliptic Equations -- Nonlinear Elliptic Equations -- Energy Methods for Evolution Problems -- Semigroup Methods Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics. This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in chapter 10, and the necessary tools from functional analysis are developed within the coarse. The book can be used to teach a variety of different courses. This new edition features new problems throughout, and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded HTTP:URL=https://doi.org/10.1007/b97427

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