ISBN0534392008

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.

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.

This book has been, unfortunately, my first introduction to numerical analysis. I wish that I could have chosen a superior book myself, but this is the one prescribed by the university I attend.

The examples in this book are mostly short and insufficient, especially when they are most needed. The lack of good examples wouldn't be so much of a problem, however, if the text itself were better. Unfortunately, many topics are poorly explained. The notation used in this book is often awkward and confusing.

I'm used reading math textbooks and understanding them. Unfortunately, Numerical Analysis by Burden and Faires expects the reader to understand concepts that aren't even fully explained in the text. Avoid if you can.

If you are studying Maths and you just want to buy a book to read before you fall asleep, then don't choose this book. You need a lot of time to read and understand this book. You will enjoy more and more when you understand every lines in this book.

The problems in this book are close to what you have to know in order to pass the course. Numerical Analysis is actually more fun and interesting than other maths courses such as linear algebra, complex variables, probability (with me).

In my opinion, the worst part of this book is the CD. It will not help anyone who do not know how to code. Instead of giving the straight code (simple code that you will be able to keep track in every line), the author made the code become a program and the input is hard to understand. So if you are not familiar with coding, then you will have a hard time figure out how these codes actually work.
Actually, somehow I think the author wants to use Maple as his coding language, but in my class, we use Mathematica, so it's a little bit different in syntax.
However, these codes cover almost all of algorithms mentioned in the book.

Well, I must start by saying I wasn't sure between the 3 and 4 stars.
Definitely not 5, definitely not 2.

The thing is, it's an introduction! Some say it's written from a mathematical viewpoint, but I didn't find it so much. I mean, considering it's numerical analysis! You have to understand where the approximations come from.

Each chapter begins with a quite useful motivation, and each section has a set of about 20 exercises, of which the odds ones are answered. I guess you have to do the basic exercises, like 2 or 3, to really grasp what's going on, but in general every topic is explained quite well.

Another 2 features, which I find excellent. The layout is very nice, does not tire you, and the text is filled with references to other books. Something like 100 other numerical analysis books and papers. This is what an introduction book is supposed to be. Gives the basics of each topic, well explained, and if you want to learn some more, or read some more proofs check the other, more specialized, references.

Finally: Yes, the price is an outrage! Do not spend these dollars or euros. I worked with the seventh edition and compared it with the new one, and there's really nothing essentially better. Basically just some historical margin notes.

In short. An introduction, of course, but easy to follow but still quite rigorous. You understand where things come from, oh, and there's the algorithms (not bad). But don't buy it for more than 70 dollars. Get an used one, or maybe the seventh edition. Just as good.