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Partial Differential Equations in Action: From Modelling to Theory
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines. The main purpose is on the one hand to train students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other hand to give them a solid theoretical background for numerical methods. At the end of each chapter, a number of exercises at different level of complexity is included
- GenresMathematics
576 pages, Paperback
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