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Numerical Methods for Scientists and Engineers (Dover Books on Mathematics) [Paperback]

R. W. Hamming
4.8 out of 5 stars  See all reviews (24 customer reviews)

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Book Description

March 1, 1987 0486652416 978-0486652412 2

Numerical analysis is a subject of extreme interest to mathematicians and computer scientists, who will welcome this first inexpensive paperback edition of a groundbreaking classic text on the subject. In an introductory chapter on numerical methods and their relevance to computing, well-known mathematician Richard Hamming ("the Hamming code," "the Hamming distance," and "Hamming window," etc.), suggests that the purpose of computing is insight, not merely numbers. In that connection he outlines five main ideas that aim at producing meaningful numbers that will be read and used, but will also lead to greater understanding of how the choice of a particular formula or algorithm influences not only the computing but our understanding of the results obtained.
The five main ideas involve (1) insuring that in computing there is an intimate connection between the source of the problem and the usability of the answers (2) avoiding isolated formulas and algorithms in favor of a systematic study of alternate ways of doing the problem (3) avoidance of roundoff (4) overcoming the problem of truncation error (5) insuring the stability of a feedback system.
In this second edition, Professor Hamming (Naval Postgraduate School, Monterey, California) extensively rearranged, rewrote and enlarged the material. Moreover, this book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include:
I. Fundamentals and Algorithms
II. Polynomial Approximation- Classical Theory
Ill. Fourier Approximation- Modern Theory
IV. Exponential Approximation ... and more
Highly regarded by experts in the field, this is a book with unlimited applications for undergraduate and graduate students of mathematics, science and engineering. Professionals and researchers will find it a valuable reference they will turn to again and again.

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Editorial Reviews

About the Author

Richard W. Hamming: The Computer Icon
Richard W. Hamming (1915–1998) was first a programmer of one of the earliest digital computers while assigned to the Manhattan Project in 1945, then for many years he worked at Bell Labs, and later at the Naval Postgraduate School in Monterey, California. He was a witty and iconoclastic mathematician and computer scientist whose work and influence still reverberates through the areas he was interested in and passionate about. Three of his long-lived books have been reprinted by Dover: Numerical Methods for Scientists and Engineers, 1987; Digital Filters, 1997; and Methods of Mathematics Applied to Calculus, Probability and Statistics, 2004.

In the Author's Own Words:
"The purpose of computing is insight, not numbers."

"There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think."

"Whereas Newton could say, 'If I have seen a little farther than others, it is because I have stood on the shoulders of giants, I am forced to say, 'Today we stand on each other's feet.' Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way."

"If you don't work on important problems, it's not likely that you'll do important work." — Richard W. Hamming

Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 752 pages
  • Publisher: Dover Publications; 2 edition (March 1, 1987)
  • Language: English
  • ISBN-10: 0486652416
  • ISBN-13: 978-0486652412
  • Product Dimensions: 8.5 x 5.4 x 1.4 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (24 customer reviews)
  • Amazon Best Sellers Rank: #32,755 in Books (See Top 100 in Books)

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Customer Reviews

4.8 out of 5 stars
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Most Helpful Customer Reviews
195 of 198 people found the following review helpful
5.0 out of 5 stars The Purpose of Computing is Insight, Not Numbers March 23, 1999
By A Customer
Throughout the book, that motto is repeated.
By reading and absorbing the material in this book, the reader is left with the tools and the insights necessary to derive their own numerical methods.
No longer will numerical methods be memorized as textbook formulas -- now the reader can adapt and derive a formula to solve a specific problem, instead of trying to fit one of a small number of textbook formulas to a problem.
The distinction is made between numerical analysis and numerical methods, with emphasis on the latter.
The book is roughly divided into two parts. The first part covers classical numerical methods, using classical error analysis (truncation error, roundoff error). The second part reexamines these methods under the frequency domain, analyzing how numerical methods affect various frequencies (the "transfer function" approach).
Numerical methods are derived under an information theory model, such as by finding a quadrature formula of the highest polynomial degree of accuracy, given limited information about the function and its derivatives.
Matrices and linear systems are not discussed as much as one might expect, although one chapter convincingly leads the reader to question some classical methods.
The content is well-rounded, introducing many readers to topics such as random number generators, difference equations and summation formulas, digital filters and quantization, discrete fourier transforms and the FFT, and orthogonal polynomials. A background in calculus is all that is needed.
Many real-world examples and anecdotes are cited, but without too much detail or too many illustrations given.
This book encourages the reader to ask: "What information is available about the problem?
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37 of 37 people found the following review helpful
5.0 out of 5 stars Gives an intuitive feel for numerical methods March 10, 2006
Chances are, if you have a degree in engineering of any kind, you have seen all of the numerical methods outlined here before. However, the purpose of this book is not just to detail how to perform different kinds of calculations. Instead, the author is attempting to give you an intuitive feel for the mathematics as well.

The book starts with an essay on numerical methods that discusses the book's five main ideas starting with its motto, which is the first idea - "The purpose of computing is insight, not numbers." The second idea is that it is necessary to study families of numbers and algorithms and to relate one family to another. The third and fourth major ideas are that of roundoff and truncation error, each of which is an effect of computing on finite machines. The final main idea is that of feedback and stability, where numbers produced at one stage are looped back to feed other stages of computations, and the result may or may not be stable.

The remainder of the book then studies many families of calculations and numbers based on these insights. The book is divided into five parts - Fundamentals and Algorithms, Polynomial Approximation, Fourier Approximation, Exponential Approximation, and finally a miscellaneous section which talks about approximations to singularities, optimization, linear independence, and eigenvalues and eigenvectors of Hermitian matrices. As you can see, the idea throughout this book is that since numerical methods are the use of numbers to simulate mathematical processes, then all of these algorithms are actually approximations. Throughout the book there are clearly worked out examples with plenty of illustrations and also many exercises, some with solutions. Highly recommended.
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36 of 37 people found the following review helpful
5.0 out of 5 stars Like no other book on numerical methods I have read. August 24, 2003
I sympathise with the reviewer who said this is one of the few
books on numerical methods he could stand. I will go further
and say this is a book that can be enjoyed. Example: section 2.8
"The Frequency Distribution of Mantissas" explains why the
leading digits of of decimal numbers are not uniformly
distributed, a result that is surely counterintuitive. There is
much more material of interest in this book too. It does
contain standard material too but is more readable than many
books. The author offers much practical advice and insight.
(Hamming is a famous name in applied mathematics and electical
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83 of 93 people found the following review helpful
5.0 out of 5 stars Can numerical analysis be fun? July 23, 1998
By A Customer
This is the only book on numerical methods I can stand. But, not only can I stand it: now I love it. It's one of the cleverest books I ever met. Hamming must be a genius of insight. Even if you wrote your thesis on differential equations, I bet you will be enriched by reading his considerations on them, from the numerical precision viewpoint. The same is true for Fourier methods, only much more, as this is the main topic of this surprising and wonderful book. Since then I bought every book written by Hamming during his lifespan, which is unfortunately over.
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14 of 15 people found the following review helpful
5.0 out of 5 stars A beautiful book. June 8, 2010
R.W. Hamming instantly became one of my favorite authors after I received this book in the mail. He wasn't afraid to inject his hard-earned experience into a field which even today really is in its infancy. While some of the material is dated in that if you ever are writing serious numerical code, you are very unlikely to implement many of the details in this book yourself, it is a great place to go to understand what your library is doing (or at least provide a general idea).

Hamming wrote this book during a very special period of time for mathematics and computer science. Algorithms and (numerical)mathematics were very much seen as a means to an end, and not an end themselves. Many mathematicians now will provide a numerical analysis of an algorithm, or derive a numerical algorithm only because it's the fashionable thing to do now, and it somehow enbiggens them by portraying a false sense of "application."

There is a sort of purity in this book, everything in it is a solution to what was a serious engineering problem in the implementation of numerics on computers. On top of this, it is written in an absolutely lucid style which I have found to be very characteristic of Hamming.

My favorite chapters are of course chapter 1: "An Essay on Numerical Methods", and chapter 'N+1' "The Art of Computing for Scientists and Engineers" If you bought the book and only read these two chapters, I would say you got your money's worth.
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Most Recent Customer Reviews
5.0 out of 5 stars Some rewiew !!!
Very good purchase !
1) The book is in new conditition without any damage.
2) The book arrived very very quickly. Read more
Published 3 months ago by Pietro Luigi CERRI
5.0 out of 5 stars Numerical methods
Good background to many mathematical methods you routinely need in data processing. Some real examples would be useful? though this is essentially a text book
Published 5 months ago by Ptf T. Cosgrove
5.0 out of 5 stars Insight
Hamming writes "The purpose of computation is insight, not numbers". Laudable sentiments, but does the book succeed? Read more
Published 7 months ago by Sourendu Gupta
4.0 out of 5 stars Classic book
This is classic book of numerical methods.
Every technical student MUST read this book.
This book is base of modern numerical methods and
show directions of progress
Published 7 months ago by Zboroshenko Alexander
4.0 out of 5 stars Don't be surprised
This is a reference book. You need previous applied math background to use it. It will help point out a mathematical solution other than what you may have already tried.
Published 9 months ago by Thomas
5.0 out of 5 stars Great Book!!!!
Its easy to understand most of the methods included, the math theory or explanation is quite easy to understand in most cases as oppossed to "Numerical Analysis" by L. Read more
Published 13 months ago by Ssound
5.0 out of 5 stars Book excellent
The book of excellent quality.
The product is important for my studies.
Use whenever you need to understand the science.
Published 14 months ago by Nilton Silva
5.0 out of 5 stars Insight into Numerical Analysis
I have been teaching numerical analysis for a long time now. I bought this book based on the author's name. I was not surprised to find out that my decision was totally correct. Read more
Published 17 months ago by Magdy Saeb
5.0 out of 5 stars Very good introduction
Very good introductory textbook. The text is not new but it is very well written. The author tries to remove informations that are not necessary at the moment and he concentrates... Read more
Published 17 months ago by Jiri Brozovsky
5.0 out of 5 stars Good item with reasonable price
It is a good one and a right choice for me. I also recommend everyone to purchase for this item if you need it.
Published 18 months ago by Pom
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