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008 101029s2011 xxu| s |||| 0|eng d
020 _a9781441970558
_9978-1-4419-7055-8
082 _a515.35
_223
100 _aTaylor, Michael E.
_920038
245 _aPartial Differential Equations I
_h[electronic resource] :
_bBasic Theory /
_cby Michael E. Taylor.
250 _a2nd ed. 2011.
260 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2011.
300 _aXXII, 654 p.
_bonline resource.
520 _aThe 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).
650 _aDifferential equations.
_920039
650 _aManifolds (Mathematics).
_920040
650 _aDifferential Equations.
_920041
650 _aManifolds and Cell Complexes.
_920042
856 _uhttps://doi.org/10.1007/978-1-4419-7055-8
942 _cEBK
999 _c13596
_d13596