Customer Reviews

Elementary Numerical Analysis

5 star:		(4)
4 star:		(0)
3 star:		(1)
2 star:		(2)
1 star:		(6)

 

 

Just so you know the source of this review and whether or not you should bother trusting me (hmm..maybe not?):
Ph.D. student in Statistics at Iowa State University.
B.S. Computer Science
B.A. Mathematics

Research areas: numerical analysis, analysis of large data sets, stochastic processes
Former research areas: truth maintenance systems, microarray analysis, parallel computing

Note: Not a plug. I like my job.

First off, the book's title is very appropriate. It requires extensive knowledge of calculus and linear algebra, but it uses a fairly non-rigorous "easy" approach to numerical analysis. It's not advanced enough for use in a graduate level class, even for non-majors, but it is very useful and appropriate for sophomore/junior undergraduates. Even though the approach is somewhat non-rigorous, the book doesn't avoid proofs, and though a more advanced mathematician or computer scientist would see holes, it's a book that surely feels complete to most undergraduate math/cs majors/minors.

The explanations and proofs are definitely not perfect. The proofs leave out steps that they assume readers should find obvious. Academic types like Atkinson who have spent years of research in this field often forget just how difficult these concepts are to undergraduates, so some of these "obvious" steps are not going to be obvious to all readers and should not have been omitted. Mixed in with the proofs are some straightforward explanations, but often they are not in layman's terms and I remember scratching my head at times. So I would give the explanations and proofs a C-/D+.

The author does a better job at the exercises. This is a difficult topic, so you don't want to have to work out problems that are too difficult, but some challenge is required to attain mastery of the subject. I think that this book accomplishes that goal. The problems are rarely overly difficult, and though most would be trivial to professors or professionals, they provide enough challenge to undergraduates who are new to the field. The author also does a good job at choosing problems which are relevant. This is nice since many (most, actually) mathematics books include many problems which look contrived and whose results seem meaningless. Anyways, I give the exercises an A.

The content is decent, but a LOT is left out. Traditionally, a two-semester sequence includes a class on numerical analysis as it relates to differential equations and a class on numerical analysis as it relates to linear algebra. Preceding discussion of either one of these topics is a necessary discussion of general iterative methods and analysis of computational error. This book covers all of those topics but none of them extensively. For a one-semester overview, the content is perfect and includes more than enough material. For a traditional two-semester sequence, this book is a bit skimpy. As stated before, the book is also not appropriate for graduate level classes. So if you haven't learned functional analysis, then don't worry--this book is for you. I give the content a B-/C+.

I was a bit disappointed with the computing examples. The examples were not poorly chosen, but there were not enough of them. Also, I think that they should have used a programming language which is easy to read even if you don't know the language. I give the computing examples a D+.

Even though I said that this book is inappropriate for graduate classes, it might serve as a nice reference for graduate students. I always skim through it as a review before certain classes. Though it can be nice as a refresher, a graduate student would probably be happier with something more rigorous like Peter Linz's "Theoretical Numerical Analysis: An Introduction to Advanced Techniques" (overview - very short) or Kendall Atkinson's (the author who wrote this book) "Theoretical Numerical Analysis: A Functional Analysis Framework".

Final note: To those who complain that it requires extensive knowledge of calculus, was that not a prerequisite at your school? The calculus required to understand this book and work the problems is not at a high school level, but it's nothing that a student who has passed college univariate and multivariate calculus shouldn't be able to handle.

2.5 stars

I'm biased because i had the good fortune to take Intro to Numeric Analysis from Ken Atkinson himself. I beta-tested this edition of the text, so my copy is in a loose-leaf binder.

Some reviewers have complained that the book is difficult because examples are in FORTRAN rather than C. I disagree. The real meat of the book is written in mathematical form; what source he provides is merely a convenience. When i took his class, most of the students (myself included) implemented in C rather than FORTRAN. No problem, because he was looking for correct results, not reviewing code.

And yes, this book assumes a solid knowledge of calculus, linear algebra, basic differential equations, and discrete logic. Did you think you'd be able to code mathematics without *understanding* it? If you understand the math in the first place, his implementations are very clear. If you don't understand the math, no amount of clarity will save you.

The real beauty, for me, was how he logically built a progression of topics, with each step providing the foundation for the next one. It was like seeing two years of college math in miniature.

Of course this book assumes (advanced?) knowledge of Calc 1 & 2 as well as linear algebra and preferably Dif. EQ. These are all prerequisites for the course in which the book is used. That being said, it is quite annoying when the book *completely* skips over intermediate steps involving calculus leaving the student scratching his head. I find myself with my nose more in my Calc. books trying to figure out what the steps leading to the answer rather than learning Num. Analysis. Would have been nice if at least some intermediate steps were added to most problems, but hey, this is college and hand holding should not be assumed.

There are 3 main gripes which contribute to the low rating.

1. The Cost. For the price of the book, (considering the way the material is presented (see 2.) there should be a solution manual bundled with it. (see 3.)

2. The explanations of the material is cut and dry and not verbose at all, [which adds 2 stars to an original 0 rating] however, there is usually only one example for a topic, followed by 10-15 excercises associated with that topic. This often leads to pure frustration and having to "google" for supplimentary material to help me through the problems due to the fact that the example is far more elemantary than the excercises.

3. Lack of solutions. Coupled with the lack of GOOD examples is the lack of solutions for the excercises you just struggled to drudge through. Chapters that typically have 10-15 problems, some with sub-problems in them usually have 5 or so solutions in the back. (so if there is say question 1, parts a-h, question 2, question 3 a - k....there would be a solution for question 1 part c, question 3 part g...).

If you take this course and this is the required text, pray that your professor has great lectures and notes(neither of which my prof. has) or be prepared to spend many hours on google looking for other references.

This book basically gives no proper examples and solutions. If at all there are examples, they don't show the steps in between. The problem is given and there are 2 or 3 intermediate steps and then he gives the answer to the problem, but the problem might be having around 10 or 12 intermediate steps. I din't find this book helpful at all.

The book is a chore to read. Many excersizes reference other parts of the book, requiring you to flip back and forth between sections. The proofs are almost all hand waved. The book has obvious typos as well. The book is more appropriate for a high school course than a college one- if you are a mathematician, you will find this book offensive. Buy if you need it for a class, but as a student who was subjected to this book for an entire semester, I highly recommend against using it.

Oh, and the cover is hideous.

i had the pain to use this book for my undergrad. coursework for a 200 level class at Cal Poly. Contrary to the other reviewers, i believe the exercises are mediocre, and the material presented lack depth to provide a solid grounding to numerical analysis. Codes are inconveniently written in fortran-97? instead of the more readable pseudo-code. It may provide a good application supplementary for engineering students, but i strongly advise against it for mathematics undergrads. No fun. Lots of handwaving and smoking mirrors.

This book requires mathematical maturity. In our class most people found it very difficult to read. In the Introduction it says, that book is recommended for advance undergrads or begining grad students. I do not recommend this book for anyone interested in Intro to Numerical analysis. The Prof. teaching the class often handed out his own lecture notes, to spare students the frustration of reading this book. You will need the knowlege of Linear algebra, Diff. equ and solid knowlege of calculus to be able to folow the text. However, i guess for someone with advance knowlege in math this book may seem more beneficial, and they may be able to appreciate it more then i did. Best of luck in your studies!

Being a university math major, first time in my life i have ever came across a math text with practically no solutions in the back of the book. Since the text is so complex you never know if your doing things right half the time with no answers to assure yourself. Horrible math book, made for a tough couple of months...

I used the first edition of this text as a senior in mathematics at UCSD, 1983 and have never parted with it. The exercises are difficult.

The second edition is worth 90 bucks, although the fact that it is PAPERBACK and WAY OVER PRICED just shows how corporate greed once again far exceeds the need of the students to have a good math book.

I would not recommend ordering this item unless you can wait a long time for it to be shipped. Ordered it almost two weeks ago, and every time I check on it, the shipping time frame gets moved out. If the book is back ordered and there is a problem, it would be nice if amazon was up front about it. I need this text for class and since I was counting on it from amazon, the bookstore is now sold out. If I had known there was a problem I would have paid more at the bookstore and at least been left in a lurch. I have always had good luck with amazon in the past but I must say I am exceptionally disappointed.