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Scientific Computing 2nd Edition

3.6 out of 5 stars 19 customer reviews
ISBN-13: 978-0072399103
ISBN-10: 0072399104
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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: 7.5 x 1.1 x 9.5 inches
  • Shipping Weight: 2.4 pounds (View shipping rates and policies)
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (19 customer reviews)
  • Amazon Best Sellers Rank: #65,276 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By JVerkuilen on July 22, 2006
Format: Hardcover
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.
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Format: Hardcover
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.
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Format: Hardcover
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.
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Format: Hardcover
Heath has an interesting book here. The author explains his intended audience in the introduction: Senior Undergraduates in Engineering/Math or beginning Graduate Students in Computational Science. I agree fully with his suggestion. If you are not in this category, I recommend reviewing Linear Algebra and computer programming prior to reading this book. I relied heavily on Khan Academy and MIT OpenCourseware for Linear Algebra explanations where the book skipped over details, and purchased a used copy of "Numerical Analysis - 7th (Seventh) Edition" to provide examples and pseudocode. This extra material helped me understand Heath's overly formal academic writing style.

"Scientific Computing" has some notable shortfalls. Some sections contain only mathematical proofs using meticulously chosen terms of art and excess of language. Throughout the book, extraneous vocabulary words like "idempotent" are introduced (without an appropriate definition) never to be seen again. Other sections provide barely enough detail to query the internet for a more thorough tutorial. As a result, the text always seems to have too much or too little detail, making it hard to read without reference material close-by.

Despite the shortcomings of the material layout, I believe one thing that draws professors to this book are the author's lecture slides published on his faculty website. While pre-made slides may be convenient to print for notes, it can have a negative impact on learning. If your local professor does little more than read from the author's notes (which are verbatim from the book) the learning experience can feel as flat as null space!
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