Scientific Computing

by Michael T. Heath

Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.

Genres: Science, Computer Science, Mathematics, Engineering, Textbooks, Reference, Physics

563 pages, Hardcover

First published December 1, 1996

Reviews

[Dr M · Rating 3 out of 5]

The subtitle to Heath's book on numerical methods for scientific computing is "an Introductory Survey". This is almost an auto-review. Brevity is simultaneously the book's strength and its weakness. Scientific Computing is not so much a comprehensive textbook as a collection of introductions to the central ideas of the most important, elementary numerical methods for linear algebra, calculus, differential equations and non-linear equations. As such it is a splendid work to turn to when you need to get a rough idea of available methods for any given type of problem, or when you need a quick overview of the basics of some method. However, the descriptions Heath gives us are so brief and lacking in details, examples and explanations that any in-depth learning, let alone understanding becomes well nigh impossible. Also, this book gives very few hints on how to implement the methods in practice.

While Scientific Computing quickly becomes insufficient as a stand-alone resource for numerical methods, this should not be taken to mean that the book is bad. It certainly is not; it is very useful for quickly reading up on a (set of) method(s). Often, this is all one needs, while on other occasions, it serves as a useful guide to what to read in-depth about in more detailed texts.

Scientific Computin deserves its place on the shelf beside my computer at work and is often the first book I turn to. There are probably several other, and possibly newer, books on numerical analysis that can serve the same purpose, but I like Scientific Computin because Heath avoids the mistake of trying to do everything. The book calls itself an introductory survey, and that is exactly what you get, nothing more (though sometimes a little less, but I can live with that if I also have access to other texts).

[Antonietta · Rating 5 out of 5]

Great book about numerical analysis. Favorite quote: "We cannot live without approximations"! :)

[Gregory · Rating 4 out of 5]

This is not a bad text book. It covers a lot of material and is pretty general. However there are also a lot of examples to help make things concrete. My only compliant was there are a good number of typos. Since this is the sort of thing I don't normally notice I figure there must be a lot more than I saw.