Customer Reviews

Schaum's Outline of Numerical Analysis

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Looking for a supplementary text for my Numerical Analysis course, I had my students pick up this text- I have found that other Outlines give a lot of excellent worked examples and provide good summaries- Not this text. If you are a beginning student, go get yourself a real text (I would highly recommend Burden and Faires, or the new text by Tim Sauer). This text offers little to no insight into the algorithms or the analysis, and spends way too much space on one dimensional interpolation problems. If you're simply looking for summaries of algorithms and practical advice on implementation, a much better text is the "Numerical Recipes" books. In summary, I'm not sure who the audience is for this book- There are many, much better, options out there.

I've had this outline for years. My only complaint about Schaum's is that sometimes their answers are not in enough detail and their indexes are skimpy. Outlines live and die based on their detailed solutions to solved problems and their index. This particular outline is excellent. All the basic numerical methods are presented with the standard format: theory, solved problems, problems with answers. What could be added, either here, or in future text (separate) would be an optimization methods section: differential search, Hooke & Jeeves min./max. search and the Golden Mean search. The later, especially, is easy to program into Excel so it would useful to show the pitfalls in these methods. All in all, this is a text you want in your engineering collection for those problems that require detailed analysis.

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Scheid gives us a broad range of methods in numerical analysis. The 846 problems can certainly keep you busy. Plus, the book is also useful as a concise summary of the most common and useful methods in the field. Students of maths, physical sciences and engineering should already be familiar with several of the methods. Like performing numerical integration or differentiation, because these mathematical steps are the fundamental calculus operations, and those fields all use these. So too is finding roots of equations, and for this, there is a chapter on Newton's method. Which tends to assume that you have an analytic form for the function and for its derivative, where you want the roots of the function.

The book also supports statistics. Unsurprisingly, since statistics is inherently about numerical evaluations. So we have least squares methods of curve fitting, and Monte Carlo methods, where the latter can also be used for numerical integration.

Ironically, while the Monte Carlo is described, the book is somewhat weak on methods for generating random numbers. And how to measure the "randomness" of such algorithms. For this, I suggest you turn to "The Art of Computer Programming" by Donald Knuth. He has an excellent length discussion on the subject.

Curve fitting is also discussed in a chapter on splines. You may already be acquainted with these, in the context of graphics packages which can fit B splines to data points.

With no previous background in numerical analysis, I bought this book on the recommendation of my boss who loved the first edition.
I had also ordered a whole lot of other books (many from Dover editions). It turns out this is the one I love to pick up from time to time so as to learn a new idea.
It goes straight to the point and gives your mind something to munch on.
I suppose that with time I'll be completing with some of my other books, to look for the rigorous proofs and so on, but for the time being this book is preparing me.

there are several problems with using this book as self-study material:
1) it is dated - though published in 1989, and by definition out of date in 2010, the first 11 chapters list many techniques that even in that period are condsidered to be of historical interest in the computer age - interpolation, collocation operators etc
2) there is not a single worked example
3) the solved problems make several leaps of logic - I wouldnt have got anywhere without referencing Wikipedia, Cliffs briefs on differential equations, Schuams advanced calculus etc.
4) sometimes new formulas are actually introduced in worked problems - eg Everet's formula
5) problems are not self contained - referencing other chapters, other problems and sometimes other problems in other chapters.

In short, this book was a struggle, and although it will give you conceptualization of different techniques, it will not give you a modern or holistic perspective on the field.

This isn't a good book on how to do numerical analysis on a computer. It's more about the methods that people used to use when they did numerical analysis with pencil and paper.

This book goes into a lot of depth into how interpolation equations are derived, and into the calculus of finite differences. Personally I think that's a beautiful subject and a lot of fun, be it useful or not - that's what math is for math's sake.

I worked all of the problems in this book when I was in high school and I recognized many of the tricks when I took a combinatorics class years later.