Partial differential equations in action : from modelling to theory / Sandro Salsa, Gianmaria Verzini.
2022
QA374
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Title
Partial differential equations in action : from modelling to theory / Sandro Salsa, Gianmaria Verzini.
Author
Salsa, S., author.
Edition
Fourth edition.
ISBN
9783031218538 (electronic bk.)
3031218531 (electronic bk.)
9783031218521
3031218523
3031218531 (electronic bk.)
9783031218521
3031218523
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (xviii, 677 pages) : illustrations.
Item Number
10.1007/978-3-031-21853-8 doi
Call Number
QA374
Dewey Decimal Classification
515/.353
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 28, 2022).
Added Author
Verzini, Gianmaria, author.
Series
Unitext. Matematica per il 3+2. 2038-5757
Unitext ; 147.
Unitext ; 147.
Available in Other Form
Partial Differential Equations in Action
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Table of Contents
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.
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.