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This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition.
- Sales Rank: #59925 in Books
- Brand: Brand: Brooks Cole
- Published on: 2004-12-10
- Original language: English
- Number of items: 1
- Dimensions: 1.46" h x 8.16" w x 9.38" l, 3.55 pounds
- Binding: Hardcover
- 847 pages
- Used Book in Good Condition
About the Author
Richard L. Burden is Emeritus Professor of Mathematics at Youngstown State University. His master's degree in mathematics and doctoral degree in mathematics, with a specialization in numerical analysis, were both awarded by Case Western Reserve University. He also earned a masters degree in computer science from the University of Pittsburgh. His mathematical interests include numerical analysis, numerical linear algebra, and mathematical statistics. Dr. Burden has been named a distinguished professor for teaching and service three times at Youngstown State University. He was also named a distinguished chair as the chair of the Department of Mathematical and Computer Sciences. He wrote the Actuarial Examinations in Numerical Analysis from 1990 until 1999.
J. Douglas Faires, late of Youngstown State University, pursued mathematical interests in analysis, numerical analysis, mathematics history, and problem solving. Dr. Faires won numerous awards, including the Outstanding College-University Teacher of Mathematics by the Ohio Section of MAA and five Distinguished Faculty awards from Youngstown State University, which also awarded him an Honorary Doctor of Science award in 2006.
Most helpful customer reviews
16 of 17 people found the following review helpful.
Review of Numerical Analysis, 7th edition
By Sergio Escobedo Bocardo
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.
19 of 22 people found the following review helpful.
Numerical Analysis explained..
By James Brownlow
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.
48 of 61 people found the following review helpful.
Wordy, poor algorithms, worse code
By B. Hanks
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.
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