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Partial Differential Equations in Action: From Modelling to Theory
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.
- GenresMathematics
701 pages, Kindle Edition
First published May 5, 2004
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Displaying 1 of 1 review
December 26, 2019
My review applies to the third edition of this book, focusing specially on my experience reading chapters 6 and 7.
Against:
Too many typos, present in previous editions...
In many sections there's simply too much hand waving, for a first time student of this subject. This book would gain much by having maybe less chapters, and a more profound, and a slower pace.
Many statements( in some definitions, theorems, etc) are too imprecise, which made me recurrently search the internet for an equivalent statement. In chapter 7 later sections, for example 7.7 where we want to prove that the set of restrictions in dense in the associated Sobolev space, the author simply does a lot of hand waving, some proofs cannot even be called sketches.
Examples: 1) The statement for Riesz Representation theorem is not correct if we consider complex functions, instead of just real ones. Even though in that section the author states he's focusing on real functions, he changes focus when later on we tend to deal with Fourier transform, and complex functions
2) the common compact condition for the test functions in the notion of convergence definition for the test function space is very imprecise.
I could give many others.
If you're learning by yourself, you might be more satisfied with Evans' bible on PDE.
For:
Even though there are many flaws, I still feel I'm able to learn something by myself.
Easy to get a free copy on the internet.
Against:
Too many typos, present in previous editions...
In many sections there's simply too much hand waving, for a first time student of this subject. This book would gain much by having maybe less chapters, and a more profound, and a slower pace.
Many statements( in some definitions, theorems, etc) are too imprecise, which made me recurrently search the internet for an equivalent statement. In chapter 7 later sections, for example 7.7 where we want to prove that the set of restrictions in dense in the associated Sobolev space, the author simply does a lot of hand waving, some proofs cannot even be called sketches.
Examples: 1) The statement for Riesz Representation theorem is not correct if we consider complex functions, instead of just real ones. Even though in that section the author states he's focusing on real functions, he changes focus when later on we tend to deal with Fourier transform, and complex functions
2) the common compact condition for the test functions in the notion of convergence definition for the test function space is very imprecise.
I could give many others.
If you're learning by yourself, you might be more satisfied with Evans' bible on PDE.
For:
Even though there are many flaws, I still feel I'm able to learn something by myself.
Easy to get a free copy on the internet.
Displaying 1 of 1 review