03346nam 22005655 450 991025408500332120200703071959.03-319-48936-410.1007/978-3-319-48936-0(CKB)3710000001041187(DE-He213)978-3-319-48936-0(MiAaPQ)EBC6314452(MiAaPQ)EBC5579085(Au-PeEL)EBL5579085(OCoLC)1066180986(PPN)198340591(EXLCZ)99371000000104118720170112d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierIntroduction to Partial Differential Equations /by David Borthwick1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XIV, 285 p. 68 illus., 61 illus. in color.)Universitext,0172-59393-319-48934-8 Includes bibliographical references and index.1. 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.This 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.Universitext,0172-5939Partial differential equationsMathematical physicsPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Partial differential equations.Mathematical physics.Partial Differential Equations.Mathematical Applications in the Physical Sciences.515.353Borthwick Davidauthttp://id.loc.gov/vocabulary/relators/aut503022MiAaPQMiAaPQMiAaPQBOOK9910254085003321Introduction to partial differential equations1523402UNINA