Customer Reviews

Partial Differential Equations and Boundary Value Problems

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This text not only provides a simple and easy-to- read-the-first-time guide to solving PDEs with Fourier series, it also is chock-full with all the necessary details and includes many interesting problems. I took a course out of this book as a sophomore in college and found it very interesting and useful. The style and difficulty is very similar to a typical undergraduate ordinary differential equations book, except this is better organized.

The subjects include a small bit on characteristics for first-order equations, a chapter on trigonometric series, PDEs in rectangular, polar, and spherical systems and associated eigenfunction expansions, Sturm-Liouville theory, the fourier transform, Laplace/Hankel transforms for PDEs, grid-type numerical methods, sampling & discrete Fourier analysis, and quantum mechanics (the Schrödinger equation).

This book is definitely great for applied mathematicians, physicists, or engineers who really need a solid introduction to the topic, written by someone who knows all the details. Any treatment in "mathematical physics" courses on PDEs will fall short of this book's content.

Of particular importance are the inclusion of special sections for Bessel functions, Legendre polynomials, associated Legendre functions, spherical harmonics, etc. All the details of solution and many exercises are included.

The most interesting parts of the book are towards the end, with the Sampling Theorem and discrete Fourier transform; and the proof of Heisenberg's uncertainty principle.

This book is also useful for more theoretical mathematicians or mathematical physicists who need an introduction to PDEs before taking a more difficult course on general theory.

In short, I think that even though this book is of great utility to non-mathematicians, it is proper to learn these concepts and techniques in a proper math setting where care is taken. This text is a solid foundation for confident application and a springboard towards more advanced subjects.

Nakhle: Just a quick note to thank you for your book! It arrived Thursday, and I've been reading it and doing the exercises both on paper and in Mathematica 3.0. After a quick review of the whole book and a thorough reading of the first 70 pages so far, I can say I just love it! If I'd only had a book like this in college and graduate school I'd have become a much better electrical engineer. Yours is one of the best expositions of both Fourier series and partial differential equations I've used. Although I haven't gotten very far into the boundary value problems and the orthogonal functions areas of the book yet, my initial review indicates they will be excellent also. I am enjoying your book immensely, and I thank you very much for it. I'll update this with a more thorough review when I have a chance to finish the book, but I wanted to share my initial impressions so others might weigh them into their own decisions to get this excellent book.

This book talks basically about everything an undergraduate needs to know about partial differential equations.
It explains Fourier series and Fourier transformation very clearly and understandable for people new to it & for somebody wants a little more deep understanding of Fourier theory.
I suggest this book to any math major student and an interested engineering student in PDE.
What this book mess is proofing wave, heat equations from a physics point of view & Finite Fourier sine and cosine transformation method, hopefully that will be covered in the 3rd edition.
In general this book is really a fantastic choice and a book every math student should have.

I bought this book up here because I didn't want to get exploited by the various bookstores around my campus as I was as a freshman, and I've gotta say that the thorough quality of work in this book probably saved my grade in my PDE class, because the professor I had was not the greatest professor in the world whether it be in his ability to accurately enunciate anything in the English language, or his unwillingness to deviate from the notes he'd developed for teaching the class after quite a number of years. It was bought used, but came to me in great condition. I'd recommend the book to anyone looking for a kickstart in PDE - the BVP problems were very straight-forward as well.

I think this book is Possibly the best Mathematic book for Engineer I've ever read. This is due to the fact that the material is so much clear and the examples are so easy to follow. The book's explanation is precise and accurate. The exercises on every chapter are helpful. I practise almost most of the exercise problems. In fact, I score an "A" on the first Test. I will recommend it to everyone without hesitation.

I just finished a PDE course using this book, in fact I attend the University where the author teaches and took the course below his office everyday. I would like to agree with the above praise of the book and the author