Projects in Scientific Computation / Edition 1

Projects in Scientific Computation / Edition 1

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by Richard E. Crandall
     
 

This interdisciplinary book provides a compendium of projects, plus numerous example programs for readers to study and explore. Designed for advanced undergraduates or graduates of science, mathematics and engineering who will deal with scientific computation in their future studies and research, it also contains new and useful reference materials for researchers.

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Overview

This interdisciplinary book provides a compendium of projects, plus numerous example programs for readers to study and explore. Designed for advanced undergraduates or graduates of science, mathematics and engineering who will deal with scientific computation in their future studies and research, it also contains new and useful reference materials for researchers. The problem sets range from the tutorial to exploratory and, at times, to "the impossible". The projects were collected from research results and computational dilemmas during the authors tenure as Chief Scientist at NeXT Computer, and from his lectures at Reed College. The content assumes familiarity with such college topics as calculus, differential equations, and at least elementary programming. Each project focuses on computation, theory, graphics, or a combination of these, and is designed with an estimated level of difficulty. The support code for each takes the form of either C or Mathematica, and is included in the appendix and on the bundled diskette. The algorithms are clearly laid out within the projects, such that the book may be used with other symbolic numerical and algebraic manipulation products

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Product Details

ISBN-13:
9780387978086
Publisher:
Springer New York
Publication date:
02/28/1994
Edition description:
1st ed. 1994. Corr. 2nd printing
Pages:
470
Product dimensions:
7.27(w) x 9.60(h) x 1.54(d)

Table of Contents

Preface
1Numbers everywhere: Selected topics in numerical analysis1
1.1Numerical evaluation2
1.2Equation solving32
1.3Random numbers and Monte Carlo42
2Exploratory computation: Collected intra- and interdisciplinary projects51
2.1Mathematical problems52
2.2Nature-motivated models68
2.3Projects from biology79
2.4Projects from physics and chemistry92
3The lure of large numbers: Projects in number theory113
3.1Large-integer arithmetic114
3.2Prime numbers117
3.3Fast algorithms129
3.4Factoring136
4The FFT forest: The ubiquitous FFT and its relatives151
4.1Discrete Fourier transform152
4.2FFT algorithms165
4.3Real-valued transforms182
4.4Number-theoretic transforms193
5Wavelets: Young arrivals in the transform family197
5.1Chords, notes, and little waves199
5.2Discrete wavelet bases205
5.3Discrete wavelet transform216
6Complexity reigns: Chaos & fractals & such229
6.1Chaos230
6.2Fractals254
7Signals from the real world: Projects in signal processing293
7.1Data compression294
7.2Sound307
7.3Images317
Appendix: Support code for the book Projects331
References447
Index457

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