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＜電子ブック＞
Partial Differential Equations in Action : From Modelling to Theory / by Sandro Salsa, Gianmaria Verzini
(La Matematica per il 3+2. ISSN:20385757 ; 147)

版	4th ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XVIII, 677 p. 1 illus : online resource
著者標目	*Salsa, Sandro author Verzini, Gianmaria author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Functional analysis LCSH:Mathematical physics FREE:Differential Equations FREE:Mathematical and Computational Engineering Applications FREE:Functional Analysis FREE:Mathematical Methods in Physics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-21853-8

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