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Fourier Series and Boundary Value Problems (Brown and Churchill), by James Brown
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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. The book is a thorough revision of the seventh edition and much care is taken to give the student fewer distractions when determining solutions of eigenvalue problems, and other topics have been presented in their own sections like Gibbs' Phenomenon and the Poisson integral formula.
- Sales Rank: #709451 in eBooks
- Published on: 2011-02-08
- Released on: 2011-02-08
- Format: Kindle eBook
About the Author
RUEL V. CHURCHILL (University of Michigan)
Most helpful customer reviews
9 of 10 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 5 people found the following review helpful.
excellent textbook
By Shashank (Shanky) Tiwari
If you are an advanced undergraduate student or a begining graduate student and want to learn not only the concepts behind Fourier Series but see how it can be applied to boundary value problems of mathematical physics, then this is "the" book you should read. It is well written - easy to understand and illustrated with lots of examples.
1 of 1 people found the following review helpful.
Complex
By Murdock Cope
One of the better Fourier Series and Boundary Value Problem texts available. A must for those interested in upper level mathematics.
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