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＜電子ブック＞
Partial Differential Equations I : Basic Theory / by Michael E. Taylor
(Applied Mathematical Sciences. ISSN:2196968X ; 115)

版	2nd ed. 2011.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2011
本文言語	英語
大きさ	XXII, 654 p : online resource
著者標目	*Taylor, Michael E author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Manifolds (Mathematics) FREE:Differential Equations FREE:Manifolds and Cell Complexes
一般注記	The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, the space of pseudodifferential operators of harmonic oscillator type, and an index formula for elliptic systems of such operators. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (SIAM Review, June 1998) HTTP:URL=https://doi.org/10.1007/978-1-4419-7055-8

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