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Partial Differential Equations in Action = From Modelling to Theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Partial Differential Equations in Action/ by Sandro Salsa, Gianmaria Verzini.
其他題名:	From Modelling to Theory /
作者:	Salsa, Sandro.
其他作者:	Verzini, Gianmaria.
面頁冊數:	XVIII, 677 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematical Methods in Physics. -
電子資源:	https://doi.org/10.1007/978-3-031-21853-8
ISBN:	9783031218538

Partial Differential Equations in Action = From Modelling to Theory /
Salsa, Sandro.

Partial Differential Equations in ActionFrom Modelling to Theory /[electronic resource] :by Sandro Salsa, Gianmaria Verzini. - 4th ed. 2022. - XVIII, 677 p. 1 illus.online resource. - La Matematica per il 3+2,1472038-5757 ;. - La Matematica per il 3+2,84.

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.

ISBN: 9783031218538

Standard No.: 10.1007/978-3-031-21853-8doiSubjects--Topical Terms:

670749
Mathematical Methods in Physics.

LC Class. No.: QA370-380

Dewey Class. No.: 515.35

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