Schaum’s Outline of Fourier Analysis with Applications to Boundary Value Problems
By addebook • Jun 28th, 2008 • Category: Mathematics •
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Schaum’s Outline of Fourier Analysis with Applications to Boundary Value Problems
Publisher: McGraw-Hill
Number Of Pages: 208
Publication Date: 1974-03-01
Sales Rank: 236220
ISBN / ASIN: 0070602190
EAN: 9780070602199
Binding: Paperback
Manufacturer: McGraw-Hill
Studio: McGraw-Hill
Average Rating: 4
Ace your course in Fourier analysis with this powerful study guide! With its clear explanations, hundreds of fully solved problems, and comprehensive coverage of the applications of Fourier series, this useful tool can sharpen your problem-solving skills, improve your comprehension, and reduce the time you need to spend studying. It also includes hundreds of additional practice problems for you to work on your own, at your own speed to help you get ready for tests. Featuring theorem proofs as well as real-world application examples, this comprehensive guide is also the perfect tutor for brushing up for graduate or professional exams!
Review:
Good for Fourier analysis and much more
This Schaum’s outline is unique in that you not only get a thorough coverage of Fourier analysis, but of other orthogonal functions such as Bessel, Legendre, Hermite, and Laguerre. The first chapter would be interesting to students of partial differential equations because of its excellent treatment of boundary value problems and of the different types of partial differential equations. It makes an interesting first taste of PDE solution methods. Chapter two is a traditional treatment of Fourier series and its applications. As in the first chapter, it is the applications that make the chapter unique as the Fourier series is used to solve problems in heat flow, Laplace’s equations, and vibrating systems. Chapter three has a good discussion of why you would actually care if a function is orthogonal. Chapter four discusses special functions and how they are evaluated. Chapters five and six are all about applications of the Fourier integral and of the Bessel function respectively. Chapter seven uses the Legendre functions to solve problems such as finding the potential interior and exterior to a sphere given a specific charge distribution. Chapter eight finishes the guide with a discussion of Hermite and Laguerre polynomials, more from a properties standpoint than from an applications standpoint. The reader of this guide should already be knowledgeable of Calculus and differential equations, and should probably have some kind of background in physics or engineering to get the most from the book. It would be a good supplement for the student of partial differential equations or signal processing as well as the student of Fourier analysis. I think what really sets this book apart is its ability to act as a stand-alone guide to the student with the required prerequisites and to actually to inspire you to study applied mathematics more. As for my own story, I picked up a previous edition of this book 17 years ago for a coworker that thought it might be helpful in a class he was taking. He decided he didn’t want it and so I began thumbing through it. I found the applications sections to be so interesting and inspiring that I wound up going back to graduate school and eventually picked up three master’s degrees! If you like this Schaum’s outline, you might also want to pick up “Schaum’s Outline of Advanced Mathematics for Engineers and Scientists” by the same author. It is also full of mathematics inspired by real world problems in need of solution.
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