Customer Reviews

Scientific Computing

5 star:		(4)
4 star:		(4)
3 star:		(1)
2 star:		(1)
1 star:		(3)

 

 

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.

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.

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.

I had to purchase this textbook when a PhD candidate was assigned to teach Scientific Computing to undergraduates. Previously, the textbook for scientific computing was by Timothy Sauer Numerical Analysis with CD-ROM.

I am having troubles with problem solving from day one because of the format of this book. This books contains long theories with zero real world application including problem solving for the students. Most of the solved problems given in the book do not have even a problem statement. The author assumes that students will figure out the problem statement based on the answer and method of problem solving!!! This book does not supply answer to any exercise let alone the solution manual.

The author does not make any effort to explain the concepts to the students as if it were a scientific publication instead of an academic textbook. I went through several theories, and I noticed that none of them offers any insights to problem solving. I have to get the help from the book mentioned above to understand the concepts. If you have a choice to buy a book on scientific computation as a student, or even as a professor to teach from a textbook, this book will be your last choice.

I am a junior in the aerospace engineering, and this is the worst text book I have seen so far in my academic life.

As a student I have found this book extremely difficult to learn from. I am a junior in mechanical engineering and have already taken classes concerning differential equations, partial differentials and some linear algebra so a lot of the basic concepts of this book are not new to me. The author seems rushed to introduce as many theories as possible into each chapter and misses many of the key qualities that make some of my other text books great learning tools.

1. Lack of examples concerning new theories.
2. Too many steps skipped in solving examples where the theory was just introduced
3. Useful equations not numbered.
4. No chapter summary with chapter highlights.
5. No chapter equation/useful formula summary.
6. No solutions in the back of the book. This makes it very difficult to study by yourself.

It is obvious that this book is very comprehensive and that most of what an engineer would ever need to know on Numerical Methods is discussed in some form. However, the "text book" side is lacking and needs a major overhaul to become a great learning tool.

This text reads well, and does a good job covering the important concepts in scientific computing. The only thing I've noticed is sometimes missing specific examples. Sometimes the sample problems are not clear as to what is expected...

Overall, its a text that is good to learn from, but maybe not the best for practice

(note: i have not yet worked through the computer programming example, these look promising)

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.

This book is a great buy for advanced mathematics and computing theories. However I have heard several people say they don't know how to use the book and can't decipher it. The book itself does not have enough explanation to be able to use it by yourself (in my opinion). But with a good teacher that can explain the small tips that a book will not publish, this book can be a great tool in the learning process.

If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.

Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.

He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.

I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.

This is the best book about scientific computing. It is very easy to understand. The examples are very explainable and have everything that covers scientific computing. Definitely a must buy.