Partial Differential Equations in Action : From Modelling to Theory / / by Sandro Salsa, Gianmaria Verzini

• Autore: Salsa S.
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
• Edizione: 4th ed. 2022.
• Descrizione fisica: 1 online resource (692 pages)
• Disciplina: 381; 515.353
• Soggetto topico: Differential equations; Engineering mathematics; Engineering - Data processing; Functional analysis; Mathematical physics; Differential Equations; Mathematical and Computational Engineering Applications; Functional Analysis; Mathematical Methods in Physics
• Persona (resp. second.): VerziniGianmaria
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Partial differential equations in action
• ISBN: 3-031-21853-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910634038403321
• Lo trovi qui: Univ. Federico II
• Serie: La Matematica per il 3+2, . 2038-5757 ; ; 147