Numerical Analysis (Hardcover)

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.

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.

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.