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13 of 14 people found the following review helpful
4.0 out of 5 stars 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...
Published on December 12, 2002 by Sergio Escobedo Bocardo

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48 of 61 people found the following review helpful
2.0 out of 5 stars 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...
Published on July 7, 2002 by B. Hanks


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13 of 14 people found the following review helpful
4.0 out of 5 stars Review of Numerical Analysis, 7th edition, December 12, 2002
This review is from: Numerical Analysis (Hardcover)
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.
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18 of 21 people found the following review helpful
4.0 out of 5 stars Numerical Analysis explained.., December 7, 1999
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This review is from: Numerical Analysis (Hardcover)
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.
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48 of 61 people found the following review helpful
2.0 out of 5 stars Wordy, poor algorithms, worse code, July 7, 2002
By 
B. Hanks (Texas, United States) - See all my reviews
(REAL NAME)   
This review is from: Numerical Analysis (Hardcover)
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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14 of 17 people found the following review helpful
3.0 out of 5 stars full of errors, April 8, 2003
By A Customer
This review is from: Numerical Analysis (Hardcover)
I normally don't write reviews for books, but I felt compelled to say that this book has quite a few errors that I've personally found quite annoying. The errors aren't mentioned in the authors' online errata either, which covers only the 1st printing. I'd think you could iron out most bugs after 7 editions, but apparently not. The coverage of material itself, while not great, is acceptable, but there are random errors scattered throughout that threw me off. At least a few of the algorithms, when implemented, don't work properly. Some of the solutions in the back aren't accurate or are just wrong (e.g., some ask for what h you need to be below a certain error bound, then proceed to give a larger h than is really necessary). Just my two cents.
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5 of 5 people found the following review helpful
5.0 out of 5 stars It's engineering-oriented, not science-oriented., January 24, 2007
By 
I. Chiang (Silicon Valley, CA, USA) - See all my reviews
(REAL NAME)   
This review is from: Numerical Analysis (Hardcover)
There are two aspects for this topic. Would you like the deeper reason why a certain way works? Or would you like to have some impressions with a certain method and try to implement it? Not many books can balance these two aspects very well and Burden's book is more toward the latter. This can be observed that almost every method is with a pseudo code and many numerical examples are given (many are even in a step-by-step way).

So if one's background is from science such as math or physics, s/he probably regards this book as a failure. For engineering students, especially undergraduates, this book seems to stay at a good balance since it doesn't get too involved.

The pseudo codes are in general well written and helpful. I think it is the strength of this book. There are few books doing better in this aspect than this book. I have one impressive experience about it. Once a graduate student asked me a question and I told him Burden's book can solve his problem. He succeeded very fast and told me he even didn't know how that method works but just did programing based on the pseudo code. For education aspect, of course we don't encourage this kind of working. But for some situations, we need it.

On the other hand, this book is rather elementary than advanced. And I think it is intended for undergraduates, not graduates. This book was my textbook of numerical analysis when I was a junior. It also served as a textbook when I lectured to undergraduate students during pursuing my phd degree in engineering. I will still use it as the textbook next time whenever possible.

I should give it 4 stars or 4 and a half at most for this book. 5 stars are just out of viewpoint balance.
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8 of 9 people found the following review helpful
3.0 out of 5 stars Middle of the Road, May 21, 2002
By A Customer
This review is from: Numerical Analysis (Hardcover)
This is one of those books where you have to be able to hit the ground running. The book assumes that the reader knows a great deal about calculus. Don't bother with this book if you have taken a calculus course a few years prior to taking a numerical analysis course. You are going to have to remember everything you did in class, which very little of us do. Well at least those that are not aspiring mathematicians. It's a good book for those who know their stuff. If you really need good complete examples and need some catching up on calculus then you need to go somewhere else. It has a calculus review that lasts one section and did not get me to remember anything. A nice fat calculus book is a good companion to this book.
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8 of 10 people found the following review helpful
3.0 out of 5 stars At times, it is a difficult read, October 25, 2006
This review is from: Numerical Analysis (Hardcover)
I examined this book as part of my constant quest for better textbooks. In this case, the course is a one-semester course in numerical analysis. I have been using "Elementary Numerical Analysis Third Edition" by Atkinson and Han and am generally pleased with the results. The first point to make is that this book has more material than I could ever cover in one semester, so from my perspective it is unsuitable. However, if you have a two semester sequence in numerical analysis, then it has enough material so that it could be used both semesters.

There are twelve chapters:

*) Mathematical preliminaries

*) Solutions of equations in one variable

*) Interpolation and polynomial approximation

*) Numerical differentiation and integration

*) Initial-value problems for ordinary differential equations

*) Direct methods for solving linear systems

*) Iterative techniques in matrix algebra

*) Approximation theory

*) Approximating eigenvalues

*) Numerical solutions of nonlinear systems

*) Boundary-value problems for ordinary differential equations

*) Numerical solutions to partial differential equations

with an exercise set at the end of each section and the solutions to the odd numbered problems included at the end.

The level is more rigorous than Atkinson and Han, more of the results are first expressed in the form of theorems as opposed to the Atkinson approach of using worked examples. Once the theorem is presented, Burden then goes on to demonstrate by example. Burden uses Maple code to present the algorithms, which is generally understandable. Since the code is presented in snippets used to solve a specific problem, a lack of experience in Maple is not a serious hindrance. It is easy to infer the meaning of the Maple commands from the context.

However, it lacks the easy readability of the Atkinson book. There were many occasions when I stopped and had to think about what I had read. It eventually made sense, but I had to think about it before it was clear. I don't have that problem with the Atkinson book. Therefore, even if we made a change to a two semester sequence in numerical analysis, I doubt if I would adopt this book.
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5 of 6 people found the following review helpful
3.0 out of 5 stars Middle of the Road, May 21, 2002
By A Customer
This review is from: Numerical Analysis (Hardcover)
This is one of those books where you have to be able to hit the ground running. The book assumes that the reader knows a great deal about calculus. Don't bother with this book if you have taken a calculus course a few years prior to taking a numerical analysis course. You are going to have to remember everything you did in class, which very little of us do. Well at least those that are not aspiring mathematicians. It's a good book for those who know their stuff. If you really need good complete examples and need some catching up on calculus then you need to go somewhere else. It has a calculus review that lasts one section and did not get me to remember anything. A nice fat calculus book is a good companion to this book.
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5 of 6 people found the following review helpful
4.0 out of 5 stars Good introductory text, August 11, 1999
By A Customer
This review is from: Numerical Analysis (Hardcover)
This text is very good for introducing the reader to many different concepts in numerical analysis. The book is definitely written from a mathemetician's point of view. If you just need algorithms and aren't looking for the math behind them... I wouldn't reccomend this book, but if you are looking to understand what makes an algorithm work and the tools to know why one algorithm will perform better for your problem than another, I heartily reccomend this book as a good text to start from. One of the best tools included in this book is a large and complete Bibliography which will lead readers yearning for more information on a given topic to good sources. Enjoy
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21 of 29 people found the following review helpful
5.0 out of 5 stars Very moderate calculus is all it takes, August 9, 1999
By A Customer
This review is from: Numerical Analysis (Hardcover)
Anyone who thinks this book is too difficult and/or requires a Ph.D. in mathematics has simply never learned any math, such as calculus and linear algebra. In that case, it's indeed easier to simply buy software that implements all the necessary numerical algorithms. This book is not a set of instructions for using a calculator, it is a book for an intelligent reader who thinks creatively and wants to understand the logic behind classical numerical methods.
Very transparent, clear, and straight to the point this book is all I needed to quickly learn about the Gaussian quadrature and understanding both the algorithm itself as well as WHY IT WORKS AND DOES SO EFFICIENTLY. Please disregard the previous author's review, as its poisonous tone alone should suggest that he is trying to blame his own mathematical deficiencies upon the authors of this very worthwhile text.
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Numerical Analysis
Numerical Analysis by Richard L. Burden (Hardcover - December 10, 2004)
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