LEADER 03882nam 22005775 450 001 9910770248903321 005 20240403181405.0 010 $a3-031-33859-6 024 7 $a10.1007/978-3-031-33859-5 035 $a(CKB)29310278200041 035 $a(MiAaPQ)EBC31001787 035 $a(Au-PeEL)EBL31001787 035 $a(DE-He213)978-3-031-33859-5 035 $a(EXLCZ)9929310278200041 100 $a20231206d2023 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPartial Differential Equations I $eBasic Theory /$fby Michael E. Taylor 205 $a3rd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (734 pages) 225 1 $aApplied Mathematical Sciences,$x2196-968X ;$v115 311 08$a9783031338588 327 $aContents of Volumes II and III -- Preface -- 1 Basic Theory of ODE and Vector Fields -- 2 The Laplace Equation and Wave Equation -- 3 Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE -- 4 Sobolev Spaces -- 5 Linear Elliptic Equation -- 6 Linear Evolution Equations -- A Outline of Functional Analysis -- B Manifolds, Vector Bundles, and Lie Groups -- Index. . 330 $aThe first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. In includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: ?These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.? (Peter Lax, SIAM review, June 1998). 410 0$aApplied Mathematical Sciences,$x2196-968X ;$v115 606 $aDifferential equations 606 $aManifolds (Mathematics) 606 $aDifferential Equations 606 $aManifolds and Cell Complexes 606 $aEquacions diferencials funcionals$2thub 606 $aVarietats (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aDifferential equations. 615 0$aManifolds (Mathematics). 615 14$aDifferential Equations. 615 24$aManifolds and Cell Complexes. 615 7$aEquacions diferencials funcionals 615 7$aVarietats (Matemātica) 676 $a515/.353 700 $aTaylor$b Michael E$041937 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910770248903321 996 $aPartial differential equations I$91501751 997 $aUNINA