La Matematica per il 3+2

Partial Differential Equations in Action

From Modelling to Theory

Authors: Salsa, Sandro

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  • Addresses the interplay between theory and modeling in problems arising in the applied sciences
  • Focuses on ideas and connections to concrete applications, in order to promote readers’ intuition and feel for the subject
  • Offers a variety of examples from different perspectives in applied sciences
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  • ISBN 978-3-319-15093-2
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About this Textbook

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.

About the authors

Prof. Sandro Salsa, Dipartimento di Matematica, Politecnico di Milano, Italy.

Reviews

“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)


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Table of contents (21 chapters)

Table of contents (21 chapters)

Buy this book

eBook $69.99
price for Mexico (gross)
  • ISBN 978-3-319-15093-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Partial Differential Equations in Action
Book Subtitle
From Modelling to Theory
Authors
Series Title
La Matematica per il 3+2
Series Volume
86
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-15093-2
DOI
10.1007/978-3-319-15093-2
Series ISSN
2038-5722
Edition Number
2
Number of Pages
XVIII, 701
Topics