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Fourier Series and Boundary Value Problems, by James Ward Brown, Ruel V. Churchill
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Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus. There are two main objectives of this text. The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations.
- Sales Rank: #1293126 in Books
- Published on: 2000-08-02
- Original language: English
- Number of items: 1
- Dimensions: 10.20" h x .78" w x 5.40" l,
- Binding: Hardcover
- 360 pages
Most helpful customer reviews
8 of 8 people found the following review helpful.
Excellent
By David
This book is quite thorough, but remains easy to follow (considering the material). It starts out with partial differential equations (no previous PDE experience needed) and shows where Fourier series comes from, which I found motivating since the purpose of Fourier Analysis was evident from the beginning. It then goes into making solutions of arbitrary functions out of sine and cosine functions as well as touching on other orthogonal sets.
The book's main focus is on starting with PDEs and ending with a solution of a Fourier series.
The first chapter was the hardest since the approaches to problems were much different than in calculus, but after adjusting to the material and the approaches to the problems, it gets easier!
9 of 9 people found the following review helpful.
WOW!!
By Me
So you're familiar with my background, I received a B.S. in Astrophysics and now I am a first year graduate student in an Applied Math program. I used this book as a supplementary resource when studying Partial Differential Equations - we got to Separation of Variables and then to Fourier Series. Every Physics student who graduates today has at least seen a Fourier Series (I hope). I didn't feel confident in my abilities so I bought this book to review.
Let me tell you, if this is your first time hearing about Fourier Series then this book is simply the BEST book to learn Fourier Series and much of the beautiful underlying theory behind Fourier Analysis! It's so well written and clear that I had absolutely no trouble following the text. I cannot express how clear and beautifully it is written, it is extremely rare for a math book at this level to be so vivid and eloquent! The proofs are easy to follow and the problems ease you into the subject presented in each section; which, in turn, are "bite-sized" and manageable. I studied the material by myself and walked away knowing Fourier Series.
There are plenty of good examples, the problems are great! If you're self-studying (or not) do as many of the problems as you can; if you read the previous two or three sections you should have absolutely no trouble going through the problems. Applications galore!
NOTE: This book isn't written at the graduate level, don't shy away from it because I mentioned being a grad student, I just wanted a review of Fourier Series. If I had to rate the level of the book I would say it's at a beginning upper-division level of a typical american university. If you've had a decent multi-variable calculus class, and are comfortable with partial derivatives, this book should be very comprehensible. It's clearer still to physics majors (or the like) who are more familiar with what and where specific equations apply to.
This book is beautiful, and I think it should be required reading of every physics and applied math student everywhere (maybe I'm just a little biased).
The ONLY caveat is that the Fourier Complex Series is left to problems, we don't get to use them to learn theory and get more comfortable with. This is okay since the cosine and sine series are equivalent to the complex series, it's just that the complex series is more elegant when doing problems or proving things.
5 of 6 people found the following review helpful.
Great text for an intro to pde's course!
By A Customer
My first encounter with partial differential equations was out of this book. Since then, I've had another course on pde's, and used this book as a reference quite often. Fourier Series adn Boundary Value Problems is very much like Complex Variables and Applicatoins, also by Churchill and Brown. It's accessible to a large audience. Though it would help to have had an advanced calculus course, it isn't necessary to understand the mechanics of solving pde's (namely the variables seperable cases, which is mostly what's in this book). If you're an undergraduate math, engineering or physics student, you'll probably be using this book.
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