LEADER 03346nam 22005655 450 001 9910254085003321 005 20200703071959.0 010 $a3-319-48936-4 024 7 $a10.1007/978-3-319-48936-0 035 $a(CKB)3710000001041187 035 $a(DE-He213)978-3-319-48936-0 035 $a(MiAaPQ)EBC6314452 035 $a(MiAaPQ)EBC5579085 035 $a(Au-PeEL)EBL5579085 035 $a(OCoLC)1066180986 035 $a(PPN)198340591 035 $a(EXLCZ)993710000001041187 100 $a20170112d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to Partial Differential Equations /$fby David Borthwick 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIV, 285 p. 68 illus., 61 illus. in color.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-48934-8 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- 2. Preliminaries -- 3. Conservation Equations and Characteristics -- 4. The Wave Equation -- 5. Separation of Variables -- 6. The Heat Equation -- 7. Function Spaces -- 8. Fourier Series -- 9. Maximum Principles -- 10. Weak Solutions -- 11. Variational Methods -- 12. Distributions -- 13. The Fourier Transform -- A. Appendix: Analysis Foundations -- References -- Notation Guide -- Index. 330 $aThis modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods. 410 0$aUniversitext,$x0172-5939 606 $aPartial differential equations 606 $aMathematical physics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aPartial differential equations. 615 0$aMathematical physics. 615 14$aPartial Differential Equations. 615 24$aMathematical Applications in the Physical Sciences. 676 $a515.353 700 $aBorthwick$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0503022 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254085003321 996 $aIntroduction to partial differential equations$91523402 997 $aUNINA