Product Description

The new Seventh Edition of Burden and Faires' well-respected Numerical Analysis provides a foundation in modern numerical-approximation techniques. Explaining how, why, and when the techniques can be expected to work, the Seventh Edition places an even greater emphasis on building readers' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. Applied problems from diverse areas, such as engineering and physical, computer, and biological sciences, are provided so readers can understand how numerical methods are used in real-life situations. The Seventh Edition has been updated and now addresses the evolving use of technology, incorporating it whenever appropriate.

Product Details

• Amazon Sales Rank: #607838 in Books
• Published on: 2000-12-29
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 864 pages

About the Author
Richard L. Burden is a Professor of Mathematics at Youngstown State University. His research interests include numerical linear algebra and numerical solution of partial differential equations.

Customer Reviews

Wordy, poor algorithms, worse code
Like other reviewers, I'm still struggling to find a decent advanced mathematics textbook. Some of the problems with Burden's book includes insufficient examples and explanations. He introduces strange and unnecessary notation in his algorithms; for example in chapter 7 (Iterative techniques for solving linear systems) many of his index loops run from 1 to n. If he set them from 0 to n-1, it would clean up much of his logic. He also apparently loves the variable XO to represent the initial approximation x naught.

Maybe due to my physics background, but his notation of representing indexes of variables as a _power_ is confusing:
Burden represents the i-th index of x as x^(i), not to be confused the i-th power of x: x^i. Modern typesetting includes subscripts, why not use them instead? Heck, use LaTeX and do the same thing (x_i)!

Finally, several of the codes on the included CD refused to run, and some of them didn't give correct answers. You will need some programming experience to edit, as none of the codes (at least all of the Matlab and possibly all of the C) adhere to any programming standards or formatting. Mr. Burden (or his programmer) is invited to purchase and use Steve McConnell's "Code Complete"--or hire someone who knows how to write maintainable code well. What is the purpose of supplying code if it cannot be used in other projects? "Gee Wiz, the book includes Code!" one might exclaim. "But what good is it?" is the inevitable response.

Numerical Analysis explained..
I use this book in a two-semester class on Numerical Analysis that I teach at Chapman University. I like the book. It starts with root-finding and interpolation algorithms, progresses to numerical estimates of derivatives and integrals. Each section is typically accompanied by the relevant algorithm(s) in pseudo-code, which I find easily translate to C or C++. Examples in Maple are given, and I've used MATLAB as well in conjunction with the book.

I rated the book with 4 stars instead of 5 for minor reasons. For example, I think a clearer description of Gaussian Quadriture could be presented, and there are other Quadriture methods that could be presented (Chebychev, Laguerre). Rational polynomial interpolation should be included as a topic. The chapters on numerical solution of differential equations are particularly good. The text developes Runge-Kutta (2nd and 4th orders) and shows how RK is used to solve systems of ODEs or higher-order DEs by introducing intermediate variables. Algorithm 5.7 (page 320) is an implementation of the solution of 'm' linear DEs that is quite simple if one uses function pointers.

The chapters on linear algebra are quite good as are the sections on approximation.

One feature of the text I find helpful is the "real world" engineering problems that are included.

Review of Numerical Analysis, 7th edition
This is a numerical analysis book written from a mathematician's point of view, and requires from the reader a good background in calculus and linear algebra.

Even though the book has an initial chapter ("mathematical preliminaries"), reading this chapter is not enough if the student has not a good previous mathematical knowledge.

The book introduces modern approximation techniques and explains how, why and when these techniques are expected to work, and allows the reader to understand why one algorithm works better than other for a given problem.

The text contains many examples as well as application problems in various areas of science and engineering.

The book uses Maple as the standard software for symbolic and approximate calculus, even though Mathematica and Derive are mentioned too and could be used instead with small modifications.

The original English edition (7th edition) includes a CD-ROM with all the algorithms, expressed in different formats (C, Fortran, Pascal, Maple, Mathematica and MATLAB), although the Spanish translation (edited by Thomson Learning) does not include the CD-ROM. However, there is an Internet address in which the CD-ROM contents can be accessed.

To conclude, the book is a good text that requires a mathematical background from the reader and covers a broad range of modern approximation techniques. It is not a mere numerical methods cookbook, but a text that analyzes and applies the numerical methods instead.