Scientific Computing (Hardcover)

by Michael T. Heath (Author) "The subject of this book is traditionally called numerical analysis..." (more)
Key Phrases: successive parabolic interpolation, relative forward error, propagated data error, Review Questions, Monte Carlo, Newton's Second Law (more...)

Editorial Reviews

Product Description
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.

Product Details

• Hardcover: 563 pages
• Publisher: The McGraw-Hill Companies, Inc.; 2nd edition (July 17, 2002)
• Language: English
• ISBN-10: 0072399104
• ISBN-13: 978-0072399103
• Product Dimensions: 9.4 x 7.4 x 0.6 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.3 out of 5 stars See all reviews (7 customer reviews)
• Amazon.com Sales Rank: #233,358 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

18 of 19 people found the following review helpful:

5.0 out of 5 stars very nice conceptual overview, July 22, 2006

By	J. Verkuilen (New York, NY United States) - See all my reviews (REAL NAME)

Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.

12 of 15 people found the following review helpful:

4.0 out of 5 stars A Good Introductory Survey, November 4, 2002

By	Edward J Gorcenski (Troy) - See all my reviews

This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.

3 of 3 people found the following review helpful:

4.0 out of 5 stars good introduction to numerical analysis, December 7, 2008

By	Lance C. Hibbeler - See all my reviews (REAL NAME)

The reviewers that give low-star reviews seem to be missing the subtitle of the book: "an introductory survey." The first two sentences of the preface explain Heath's standpoint for the entire book- a broad overview of numerical methods, with focus on the ideas behind the algorithms rather than detailed analysis. There are certainly other materials out there that go into much more depth than what Heath does, but that isn't what he was trying to do. Topics in the book include basic numerical analysis, linear equation solvers, least squares, eigenvalues, nonlinear equation solvers, optimization, interpolation, numerical integration/differentiation, IVP/BVP ordinary differential equations, partial differential equations, and briefly, FFT and random numbers.

I consider myself well-versed in numerical methods, even before reading this book. I still learned many things from the book though, which is either a "plus" for Heath or a "minus" for every other numerical analysis book I've looked through. Heath always discusses existence, uniqueness, and conditioning of problems in very well explained math- as an engineer, I found the proofs and derivations easy enough to follow. The discussion of implementation is always in pseudocode, and only hits the main points of the algorithms- this could be better by mentioning some (or more, if applicable) of the problems that come up, such as scaling and error issues.

My complaints with the book are 1) the overall organization, including the fact that all throughout the book Heath says "as seen in section x.x" (clearly, the man is a Fortran programmer- these are just GOTO statements); seriously, I know how a table of contents and an index work, 2) a lack of non-trivial examples; I think one or two big "case studies" or something similar per chapter would really help to cement the material and its implementation. Also, 3) the book is on the expensive side. I learned a lot, but if I were to normalize by cost, I didn't get much value from this purchase.

So in summary, the book is good but not outstanding (I don't think there is an outstanding broad-brush numerical analysis book yet). The math and theory is just right for people seeing this material for the first/second time. The examples are kind of lacking. If you write scientific software, this is definitely one to get.