LEADER 04255nam 22006255 450 001 9910637713003321 005 20251113185401.0 010 $a3-031-13379-X 024 7 $a10.1007/978-3-031-13379-4 035 $a(MiAaPQ)EBC7165634 035 $a(Au-PeEL)EBL7165634 035 $a(CKB)25913865700041 035 $a(PPN)267813511 035 $a(OCoLC)1357018833 035 $a(DE-He213)978-3-031-13379-4 035 $a(EXLCZ)9925913865700041 100 $a20221221d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPartial Differential Equations $eAn Introduction to Analytical and Numerical Methods /$fby Wolfgang Arendt, Karsten Urban 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (463 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v294 311 08$aPrint version: Arendt, Wolfgang Partial Differential Equations Cham : Springer International Publishing AG,c2023 9783031133787 320 $aIncludes bibliographical references and index. 327 $a1 Modeling, or where do differential equations come from -- 2 Classification and characteristics -- 3 Elementary methods -- 4 Hilbert spaces -- 5 Sobolev spaces and boundary value problems in dimension one -- 6 Hilbert space methods for elliptic equations -- 7 Neumann and Robin boundary conditions -- 8 Spectral decomposition and evolution equations -- 9 Numerical methods -- 10 MapleŽ, or why computers can sometimes help -- Appendix. 330 $aThis textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with Maple? completes the book. Throughout, three fundamental examples are studied with different tools: Poisson?s equation, the heat equation, and the wave equation on Euclidean domains. The Black?Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v294 606 $aDifferential equations 606 $aNumerical analysis 606 $aFunctional analysis 606 $aDifferential Equations 606 $aNumerical Analysis 606 $aFunctional Analysis 615 0$aDifferential equations. 615 0$aNumerical analysis. 615 0$aFunctional analysis. 615 14$aDifferential Equations. 615 24$aNumerical Analysis. 615 24$aFunctional Analysis. 676 $a515.353 700 $aArendt$b Wolfgang$f1950-$054059 702 $aUrban$b Karsten 702 $aKennedy$b James B.$f1932- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910637713003321 996 $aPartial differential equations$93090577 997 $aUNINA