Scientific Computing

by Michael T. Heath

Book Overview

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,... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: 0072399104
• ISBN13: 9780072399103
• Release Date: July 2002
• Publisher: McGraw-Hill Education
• Length: 576 Pages
• Weight: 2.35 lbs.
• Dimensions: 1.1" x 7.7" x 9.6"

Customer Reviews

Great buy

Book is in great condition, got to me in short order. Very satisfied, would buy from them again.

very well written for its purpose

This book is very well written for its purpose as an introductory textbook on scientific computing for students in computer science or engineering. There does not seem to be a comparable book in the market, so this book fills an important gap for teaching and learning in scientific computing, for computational scientists to understand when and why the numerical algorithms work. It is not designed to be an advanced textbook or reference book, but its comprehensive list of software and bibliography makes it a valuable resource for advanced researchers. Some negative reviews seems to be very unfair about the book, and frankly some of those reviews are quite naive. They seem to compare this book with numerical recipe. That is not the purpose of this book! Any well-trained numerical analyst would know that you should use existing high-quality numerical software whenever possible instead of trying to pick a piece of code from any textbook, because actual implementation of numerical algorithms can be very subtle! Even a minor change in the ordering the operations can make big differences in the stability and accuracy, not to mention other considerations such as efficiency and productivity. This book is not perfect either. In particular, its coverage on ODEs and PDEs is somewhat sparse, so for advanced numerical analysis courses some other textbook is needed to supplement it.

good introduction to numerical analysis

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.

very nice conceptual overview

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.

A Good Introductory Survey

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.