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# Numerical Methods for Scientists and Engineers

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## Description

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.

show more

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.

show more

## Product details

- Paperback | 752 pages
- 137.16 x 210.82 x 35.56mm | 793.78g
- 01 Mar 1987
- Dover Publications Inc.
- New York, United States
- English
- New edition
- New edition
- Illustrations, unspecified
- 0486652416
- 9780486652412
- 102,740

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## About Richard W. Hamming

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

show more

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

show more

## Table of contents

Preface

I Fundamentals and Algorithms

1 An Essay on Numerical Methods

2 Numbers

3 Function Evaluation

4 Real Zeros

5 Complex Zeros

*6 Zeros of Polynomials

7 Linear Equations and Matrix Inversion

*8 Random Numbers

9 The Difference Calculus

10 Roundoff

*11 The Summation Calculus

*12 Infinite Series

13 Difference Equations

II Polynomial Approximation-Classical Theory

14 Polynomial Interpolation

15 Formulas Using Function Values

16 Error Terms

17 Formulas Using Derivatives

18 Formulas Using Differences

*19 Formulas Using the Sample Points as Parameters

20 Composite Formulas

21 Indefinite Integrals-Feedback

22 Introduction to Differential Equations

23 A General Theory of Predictor-Corrector Methods

24 Special Methods of Integrating Ordinary Differential Equations

25 Least Squares: Practice Theory

26 Orthogonal Functions

27 Least Squares: Practice

28 Chebyshev Approximation: Theory

29 Chebyshev Approximation: Practice

*30 Rational Function Approximation

III Fournier Approximation-Modern Theory

31 Fourier Series: Periodic Functions

32 Convergence of Fourier Series

33 The Fast Fourier Transform

34 The Fourier Integral: Nonperiodic Functions

35 A Second Look at Polynomial Approximation-Filters

*36 Integrals and Differential Equations

*37 Design of Digital Filters

*38 Quantization of Signals

IV Exponential Approximation

39 Sums of Exponentials

*40 The Laplace Transform

*41 Simulation and the Method of Zeros and Poles

V Miscellaneous

42 Approximations to Singularities

43 Optimization

44 Linear Independence

45 Eigenvalues and Eigenvectors of Hermitian Matrices

N + 1 The Art of Computing for Scientists and Engineers

Index

* Starred sections may be omitted.

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I Fundamentals and Algorithms

1 An Essay on Numerical Methods

2 Numbers

3 Function Evaluation

4 Real Zeros

5 Complex Zeros

*6 Zeros of Polynomials

7 Linear Equations and Matrix Inversion

*8 Random Numbers

9 The Difference Calculus

10 Roundoff

*11 The Summation Calculus

*12 Infinite Series

13 Difference Equations

II Polynomial Approximation-Classical Theory

14 Polynomial Interpolation

15 Formulas Using Function Values

16 Error Terms

17 Formulas Using Derivatives

18 Formulas Using Differences

*19 Formulas Using the Sample Points as Parameters

20 Composite Formulas

21 Indefinite Integrals-Feedback

22 Introduction to Differential Equations

23 A General Theory of Predictor-Corrector Methods

24 Special Methods of Integrating Ordinary Differential Equations

25 Least Squares: Practice Theory

26 Orthogonal Functions

27 Least Squares: Practice

28 Chebyshev Approximation: Theory

29 Chebyshev Approximation: Practice

*30 Rational Function Approximation

III Fournier Approximation-Modern Theory

31 Fourier Series: Periodic Functions

32 Convergence of Fourier Series

33 The Fast Fourier Transform

34 The Fourier Integral: Nonperiodic Functions

35 A Second Look at Polynomial Approximation-Filters

*36 Integrals and Differential Equations

*37 Design of Digital Filters

*38 Quantization of Signals

IV Exponential Approximation

39 Sums of Exponentials

*40 The Laplace Transform

*41 Simulation and the Method of Zeros and Poles

V Miscellaneous

42 Approximations to Singularities

43 Optimization

44 Linear Independence

45 Eigenvalues and Eigenvectors of Hermitian Matrices

N + 1 The Art of Computing for Scientists and Engineers

Index

* Starred sections may be omitted.

show more