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Projects in Scientific Computation / Edition 1

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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

"...the soft cover version of the popular hardcover is an interdisciplinary compendium of projects, together with a large number of example programs for readers to study & explore & includes an accompanying disk."

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Product Details

  • ISBN-13: 9780387978086
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 2/28/1994
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 470
  • Product dimensions: 7.27 (w) x 9.60 (h) x 1.54 (d)

Table of Contents

Preface
1 Numbers everywhere: Selected topics in numerical analysis 1
1.1 Numerical evaluation 2
1.2 Equation solving 32
1.3 Random numbers and Monte Carlo 42
2 Exploratory computation: Collected intra- and interdisciplinary projects 51
2.1 Mathematical problems 52
2.2 Nature-motivated models 68
2.3 Projects from biology 79
2.4 Projects from physics and chemistry 92
3 The lure of large numbers: Projects in number theory 113
3.1 Large-integer arithmetic 114
3.2 Prime numbers 117
3.3 Fast algorithms 129
3.4 Factoring 136
4 The FFT forest: The ubiquitous FFT and its relatives 151
4.1 Discrete Fourier transform 152
4.2 FFT algorithms 165
4.3 Real-valued transforms 182
4.4 Number-theoretic transforms 193
5 Wavelets: Young arrivals in the transform family 197
5.1 Chords, notes, and little waves 199
5.2 Discrete wavelet bases 205
5.3 Discrete wavelet transform 216
6 Complexity reigns: Chaos & fractals & such 229
6.1 Chaos 230
6.2 Fractals 254
7 Signals from the real world: Projects in signal processing 293
7.1 Data compression 294
7.2 Sound 307
7.3 Images 317
Appendix: Support code for the book Projects 331
References 447
Index 457
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