This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages computer for illustrating results and applications, but is also suitable for use without computer access. Contains more engineering and physics applications, and more mathematical proofs and theory of partial differential equations, than the first edition. Offers a large number of exercises per section. Provides marginal comments and remarks throughout with insightful remarks, keys to following the material, and formulas recalled for the reader's convenience. Offers Mathematica files available for download from the author's website. A useful reference for engineers or anyone who needs to brush up on partial differential equations.
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Packed with examples, this book provides a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material understandable even for readers with limited exposure to topics beyond calculus. Encourages the use of computer resources for illustrating results and applications, but is also suitable for use without computer access. Includes additional specialized topics that can be read as desired, and that can be read independently of each other. Denotes exercises requiring use of a computer with computer icons, asking readers to investigate problems using computer-generated graphics and to generate numerical data that cannot be computed by hand. Offers Mathematica files for download from the author's Web site; can be accessed through the Prentice Hall address prenhall/pubguide/. For engineers or anyone looking to brush up on their advanced mathematics skills.
--This text refers to an out of print or unavailable edition of this title.
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38 of 38 people found the following review helpful:
5.0 out of 5 stars
A clear introduction to PDEs, Fourier series,
By A Customer
This review is from: Partial Differential Equations and Boundary Value Problems (Hardcover)
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.
19 of 24 people found the following review helpful:
5.0 out of 5 stars
Initial impressions,
By Bob Lyons, Jr. (Washington, D.C.) - See all my reviews
This review is from: Partial Differential Equations and Boundary Value Problems (Hardcover)
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.
2 of 2 people found the following review helpful:
5.0 out of 5 stars
Great book,
This review is from: Partial Differential Equations with Fourier Series and Boundary Value Problems (2nd Edition) (Paperback)
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.
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