Customer Reviews

Applied Numerical Analysis

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

 

 

I was quite amazed by the wide range of topics and applications covered by this book. And yet, each topic is covered in detail, with many algorithms presented to achieve a certain goal. The various algorithms are always summarised and compared, so that it is a simple matter to know which algorithm to choose depending on the circumstances of the problem at hand. I liked the very detailed examples which tend to run over a good number of iterations so that one can easily test one's understanding of the operation of the algorithm.

However, the disappointment lay in the number of mistakes that are made. Most of them are very subtle, and are only discovered if you go through the text carefully, or try to implement an algorithm based on the example pseudocode. In most cases it is the pseudocode that has gone wrong. If you are only a beginner programmer, then it will be difficult to sift through the poorly written pseudocode. On the other hand, a seasoned programmer will have no problems.

In summary - a top class book marred by some mistakes. If you know how to program, then this book is for you. Beginner programmers will be slowed somewhat by the poor pseudocode.

Using the text for self study, I was initially quite pleased. The layout is attractive, selection of topics appropriate and writing style generally clear. The applied problems are rather nice.

While the derivation of the methods and theory discussed is generally brief- the author does provide an adequate basis for a workable understanding. Exposition is appropriate (perhaps even good) for an 'applied' book.

I did, however, find the work somewhat uneven: the Newton Cotes section, for example, was a little more disorganized than I would have liked. Some simple rearrangement and grouping of thoughts would have already helped to clarify many of the ideas. Surprisingly, the previous (6th) edition seems to have done a better job in this particular case.

In any event, my largest issue with the book is the staggering number of errors. I don't use the term lightly. I've read many technical books that have a minor typo here or there: it's natural. With Applied Numerical Analysis there appears to have been little proof-reading at all!

In Chapter 3 alone I've noted more than 10 problems: some more than simple typo's. This is unacceptable for a technical work!

I spent a great deal of time and effort trying to understand many of the discussions only to eventually realize that the cause of my frustration was a fault in the text. Besides the wasted effort, this had the knock-on effect that I began to doubt everything that seemed the least bit confusing.

Publishers should be reprimanded for such lax quality control.

If you do intend to use this book, I would recommend that you try to find a comprehensive list of errata somewhere.

I've owned a copy of this since I was an undergrad back in the late 1970's when it was just in its second edition. I haven't seen a book dedicated to the teaching of numerical analysis that explains algorithms more clearly. The authors go into great detail not just on the how's but the why's - the motivation of doing things a certain way. Strangely enough, though, the numerous mistakes just get worse with age, not better. My old original second edition printed in 1980 has relatively few errors. This seventh edition has errors to the point of distraction. If you must have this for a text you might want to also pick up a copy of the very economical Introduction to Numerical Analysis: Second Edition (Dover Books on Advanced Mathematics) by Hillebrand. It's an oldie but a goodie. If you think Gerald's text is in error look up the topic in Hillebrand and insure you understand the topic. Chances are you do and there is a numerical error in Gerald's text that contradicts your own correct understanding. Finally, any student of numerical analysis simply must have a copy of Numerical Recipes 3rd Edition: The Art of Scientific Computing. That one is more of the "give a man a fish" variety and has the source code and some explanation, but is by no means a textbook.

Oddly enough the table of contents is not included in the product description for this book, so I show that next just so you'll know what you're getting

0. Preliminaries.
Analysis versus Numerical Analysis.
Computers and Numerical Analysis.
An Illustrative Example.
Kinds of Errors in Numerical Procedures.
Interval Arithmetic.
Parallel and Distributed Computing.
Measuring the Efficiency of Procedures.
1. Solving Nonlinear Equations.
Interval Halving (Bisection).
Linear Interpolation Methods.
Newton's Method.
Muller's Method.
Fixed-Point Iteration.
Other Methods.
Nonlinear Systems.
2. Solving Sets of Equations.
Matrices and Vectors.
Elimination Methods.
The Inverse of a Matrix and Matrix Pathology.
Almost Singular Matrices - Condition Numbers.
Interactive Methods.
Parallel Processing.
3. Interpolation and Curve Fitting.
Interpolating Polynomials.
Divided Differences.
Spline Curves.
Bezier Curves and B-Splines.
Interpolating on a Surface.
Least Squares Approximations.
4. Approximation of Functions.
Chebyshev Polynomials and Chebyshev Series.
Rational Function Approximations.
Fourier Series.
5. Numerical Differentiation and Integration.
Differentiation with a Computer.
Numerical Integration - The Trapezoidal Rule.
Simpson's Rules.
An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration.
Gaussian Quadrature.
Multiple Integrals.
Applications of Cubic Splines.
6. Numerical Solution of Ordinary Differential Equations.
The Taylor Series Method.
The Euler Method and Its Modification.
Runge-Kutta Methods.
Multistep Methods.
Higher-Order Equations and Systems.
Stiff Equations.
Boundary-Value Problems.
Characteristic-Value Problems.
7. Optimization.
Finding the Minimum of y = f(x).
Minimizing a Function of Several Variables.
Linear Programming.
Nonlinear Programming.
Other Optimizations.
8. Partial Differential Equations.
Elliptic Equations.
Parabolic Equations.
Hyperbolic Equations.
9. Finite Element Analysis.
Mathematical Background.
Finite Elements for Ordinary Differential Equation.
Finite Elements for Partial Differential Equation.
Appendices.
A. Some Basic Information from Calculus.
B. Software Resources.
Answers to Selected Exercises.

I have been using this book since the first edition in 1970. I have just bought the last edition, from Amazon, and found three errors in the first chapter. It should be corrected. In figure 1.2 (pag 4), the end of l1 is not right.In the same page the third formula is not right, as it should show sqr(sin) instead of sin. In page 41, the first digit (d1) would always be 1, so IEEE 754 changed a little what is presented. Even so I want to repit that this is very good book and I recommend it firmly. Raymundo de Oliveira

The quality of the book is very poor because the other copies I saw have a far better quality. I think Amazon has to improve on this aspect.

Nowadays with all the circuit and matrix computer aided systems out there, the basics of numerical methods gets overlooked. This book keeps to these fundamentals methods and is an excellent bridge between purely closed-form knowledge taught in schools and the open-form procedures quietly employed in most computer aided engineering systems.

Particularly fond of this text's discussion on boundary-value problems.

Have to agree with earlier post, book looks nice and clear but numerous errors make actually using (vs. just browsing) the material very difficult. 7th edition ADI section has numerous mislabed equations, incorrect data values, unfortunate. Suggest look elsewhere for a numerical analysis book.

This has been the best numerical analysis book that I have ever seen. The author does a brilliant job and explains concepts with extreme clarity. With this book, there isn't even any need of sitting in a professor's lecture. The book that my university uses sucks so bad, there's not 1 thing I could understand. Relying on that would have flunked me, yet that useless book costs over $100 and this remarkable book only cost me $20. It may be a 1994 edition, but even 2005 edition books on numerical analysis fail to meet its quality. Definitely a lifesaver for me.

I like this book and have been reading it since 1985. I would be very pleased,if I am able to buy the student series edition, which is much cheaper than hardcover and practical. Why don't you supply also this edition?

I found this edition of the book to be very easy to understand, especially for a novice. All of the algorithms were very helpful. The wide variety of computer examples (Matlab, Mathematica, C, etc.) that are used make the book a great tool for students.