Schaum's Outline of Fourier Analysis with Applications to Boundary Value Problems

by Murray R. Spiegel

Book Overview

Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0070602190
• Release Date: March 1974
• Publisher: McGraw-Hill Education
• Length: 208 Pages
• Weight: 0.90 lbs.
• Dimensions: 10.9" x 0.5" x 8.4"

Customer Reviews

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.

Step-by-step explanations

This text is a good supplement to understanding the use of Fourier analysis and how it is used in real-world applications. The explanations are to the point and the solved problems are all fairly easy to follow.At the end of the chapter, there are exercises to test your knowledge, and most of the answers are in the back of the book. Modeling the exercises on the problems, you can usually work out what you should do for the exercise.This is a good study guide.

Good study aid!

Very helpful to me in my medical imaging and signal processing assignments! A good buy for any student of engineering or science, particuarly useful to the study of signal analysis.