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Cover: 9783031218521 | Partial Differential Equations in Action | From Modelling to Theory
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Partial Differential Equations in Action
From Modelling to Theory
Taschenbuch von Gianmaria Verzini (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor

Sandro Salsa is a Emeritus Professor of Mathematical Analysis at Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on boundary behavior, regularity and free boundary problems. He is an author of 14 books and several papers in the most prestigious scientific mathematical journals.

Gianmaria Verzini is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan. He is author of 5 books and more than 50 papers, published on prominent international journals. His scientific interests concern the applications of Nonlinear Analysis to the existence, multiplicity, qualitative properties and regularity of solutions to nonlinear differential equations and systems.

Inhaltsverzeichnis

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.

Details
Erscheinungsjahr: 2022
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: La Matematica per il 3+2
Inhalt: xviii
677 S.
1 s/w Illustr.
677 p. 1 illus.
ISBN-13: 9783031218521
ISBN-10: 3031218523
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Verzini, Gianmaria
Salsa, Sandro
Auflage: 4th ed. 2022
Hersteller: Springer International Publishing
Springer International Publishing AG
La Matematica per il 3+2
Maße: 235 x 155 x 35 mm
Von/Mit: Gianmaria Verzini (u. a.)
Erscheinungsdatum: 09.12.2022
Gewicht: 1,163 kg
Artikel-ID: 125728440
Über den Autor

Sandro Salsa is a Emeritus Professor of Mathematical Analysis at Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on boundary behavior, regularity and free boundary problems. He is an author of 14 books and several papers in the most prestigious scientific mathematical journals.

Gianmaria Verzini is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan. He is author of 5 books and more than 50 papers, published on prominent international journals. His scientific interests concern the applications of Nonlinear Analysis to the existence, multiplicity, qualitative properties and regularity of solutions to nonlinear differential equations and systems.

Inhaltsverzeichnis

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.

Details
Erscheinungsjahr: 2022
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: La Matematica per il 3+2
Inhalt: xviii
677 S.
1 s/w Illustr.
677 p. 1 illus.
ISBN-13: 9783031218521
ISBN-10: 3031218523
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Verzini, Gianmaria
Salsa, Sandro
Auflage: 4th ed. 2022
Hersteller: Springer International Publishing
Springer International Publishing AG
La Matematica per il 3+2
Maße: 235 x 155 x 35 mm
Von/Mit: Gianmaria Verzini (u. a.)
Erscheinungsdatum: 09.12.2022
Gewicht: 1,163 kg
Artikel-ID: 125728440
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