
Partial Differential Equations in Action
From Modelling to Theory
Sandro Salsa(Author)
Springer (Publisher)
2nd Edition
Published on 19. March 2015
Book
Paperback/Softback
XVIII, 701 pages
978-3-319-15092-5 (ISBN)
Article exhausted; check for reprint
Description
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has 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 in 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 turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.
Reviews / Votes
"This book, presented at the advanced undergraduate or first year graduate level, presents a very interesting mix of physical applications and abstract theory supporting rigorous existence and regularity results for PDEs. ... Rigorous approaches, including Sobolev spaces, dual spaces, distribution theory, and weak solutions, are introduced in a transparent, well-motivated fashion, achieving a level that allows one to make contact with the professional literature." (Peter Bernard Weichman, Mathematical Reviews, May, 2016) "In this advanced textbook, Salsa (Politecnico di Milano, Italy) provides a well-written book blending abstract theory with examples. ... The author explains theory and models clearly, using techniques such as well-thought-out examples, theorems and proofs, and reader-posed questions with answers and exercises at the end of each chapter. ... Summing Up: Recommended. Graduate students and researchers/faculty." (S. L. Sullivan, Choice, Vol. 53 (4), December, 2015)More details
Series
Edition
2nd ed. 2015
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Upper undergraduate
Edition type
Revised edition
Illustrations
biography
Dimensions
Height: 23.5 cm
Width: 15.5 cm
ISBN-13
978-3-319-15092-5 (9783319150925)
DOI
10.1007/978-3-319-15093-2
Schweitzer Classification
Other editions
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12/2022
4th Edition
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Book
09/2017
3rd Edition
Springer
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E-Book
04/2015
2nd Edition
Springer
€74.89
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Previous edition

Book
12/2007
Springer
€58.84
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Person
Prof. Sandro Salsa, Dipartimento di Matematica, Politecnico di Milano, Italy.
Content
1 Introduction.- 2 Diffusion.- 3 The Laplace Equation.- 4 Scalar Conservation Laws and First Order Equations.- 5 Waves and vibrations.- 6 Elements of Functional Analysis.- 7 Distributions and Sobolev Spaces.- 8 Variational formulation of elliptic problems.- 9 Further Applications.- 10 Weak Formulation of Evolution Problems.- 11 Systems of Conservation Laws.- 12 A Fourier Series.- 13 B Measures and Integrals.- 14 C Identities and Formulas.