04221nam 22006735 450 991063403840332120251113194848.03-031-21853-110.1007/978-3-031-21853-8(MiAaPQ)EBC7156550(Au-PeEL)EBL7156550(CKB)25657527200041(DE-He213)978-3-031-21853-8(EXLCZ)992565752720004120221208d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierPartial Differential Equations in Action From Modelling to Theory /by Sandro Salsa, Gianmaria Verzini4th ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (692 pages)La Matematica per il 3+2,2038-5757 ;147Print version: Salsa, Sandro Partial Differential Equations in Action Cham : Springer International Publishing AG,c2023 9783031218521 Includes bibliographical references and index.1 Introduction -- 2 Diffusion -- 3 The Laplace Equation -- 4 Scalar Conservation Laws and First Order Equations -- 5 Waves and Vibration -- 6 Elements of Functional Analysis -- 7 Distributions and Sobolev Spaces -- 8 Variational Formulation of Elliptic Problems -- 9 Weak Formulation of Evolution Problems -- 10 More Advanced Topics -- 11 Systems of Conservation Laws -- Appendix A: Measures and Integrals -- Appendix B: Identities and Formulas.This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.La Matematica per il 3+2,2038-5757 ;147Differential equationsEngineering mathematicsEngineeringData processingFunctional analysisMathematical physicsDifferential EquationsMathematical and Computational Engineering ApplicationsFunctional AnalysisMathematical Methods in PhysicsDifferential equations.Engineering mathematics.EngineeringData processing.Functional analysis.Mathematical physics.Differential Equations.Mathematical and Computational Engineering Applications.Functional Analysis.Mathematical Methods in Physics.381515.353Salsa S.61750Verzini GianmariaMiAaPQMiAaPQMiAaPQBOOK9910634038403321Partial differential equations in action715363UNINA