Projects in Scientific ComputationThis interdisciplinary book provides a compendium of projects, together with a large number of example programs for readers to study and explore. The book is designed for advanced undergraduate or graduate students 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." These projects were collected from research results and computational dilemmas during the author's tenure as Chief Scientist at NeXT Computer, Inc. and from his scientific computation lectures in the Department of Physics 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 some combination of these, and is designed with an estimated level of difficulty. The support code for each project takes the form of either C or Mathematica, and is printing in the Appendix. The algorithms are clearly laid out within the text projects, so the book can be used with other symbolic numerical and algebraic manipulation products. |
Contents
Numbers everywhere Selected topics in numerical analysis | 1 |
Numerical evaluation | 2 |
Evaluation of famous constants | 6 |
Evaluation of elementary functions | 16 |
Special functions | 30 |
Equation solving | 32 |
Matrix algebra | 33 |
Nonlinear equation systems | 38 |
Complex FFTs N a power of 2 | 174 |
Realsignal FFTs | 177 |
FFTs for other radices | 178 |
FFTs in higher dimensions | 179 |
Applications of the FFT | 181 |
Realvalued transforms | 182 |
Hartley transform | 183 |
Discrete cosine transform | 185 |
Differential equations | 40 |
Random numbers and Monte Carlo | 42 |
Generating random numbers | 43 |
Numerical integration and Monte Carlo | 47 |
Exploratory computation Collected intra and interdisciplinary projects | 51 |
Mathematical problems | 52 |
Symbolic manipulation | 55 |
Real and complex analysis | 62 |
Naturemotivated models | 68 |
Neural network experiments | 70 |
Genetic algorithms and artificial life | 77 |
Projects from biology | 79 |
Physiology neurobiology and medicine | 84 |
Molecular biology | 89 |
Projects from physics and chemistry | 92 |
Classical physics | 93 |
Quantum theory | 102 |
Molecules and structure | 107 |
Relativity | 110 |
The lure of large numbers Projects in number theory | 113 |
Largeinteger arithmetic | 114 |
Testing the operations | 115 |
Prime numbers | 117 |
Primes in general | 120 |
Fast algorithms | 129 |
Fast mod division and inversion | 133 |
Other fast algorithms | 135 |
Factoring | 136 |
Factoring algorithms | 138 |
Status of Fermat numbers | 145 |
The FFT forest The ubiquitous FFT and its relatives | 151 |
Discrete Fourier transform | 152 |
Fundamental DFT manipulations | 155 |
Algebraic aspects of the DFT | 156 |
DFT test signals | 160 |
Direct DFT software | 162 |
FFT algorithms | 165 |
Recursive FFTs | 166 |
FFT indexing and butterflies | 167 |
WalshHadamard transform | 188 |
Squarewave transform | 191 |
Numbertheoretic transforms | 193 |
Exploring Numbertheoretic transforms | 194 |
Wavelets Young arrivals in the transform family | 197 |
Chords notes and little waves | 199 |
Windowed Fourier transform | 200 |
Continuous wavelet transform | 203 |
Discrete wavelet bases | 205 |
Example wavelet expansions | 206 |
Mother function and its wavelet | 208 |
Wavelets of compact support | 212 |
Discrete wavelet transform | 216 |
Fast wavelet transform algorithms | 222 |
Applications of fast wavelet transforms | 224 |
Complexity reigns Chaos fractals such | 229 |
Chaos | 230 |
Quadratic map algebra | 232 |
Bifurcation and chaos | 236 |
Chaos models | 240 |
Chaos stability and Lyapunov exponents | 251 |
Applications of chaos theory | 253 |
Fractals | 255 |
Theory of fractals | 258 |
Visualization of fractals | 262 |
Fractal Brownian noise | 273 |
Measurement of fractal dimension | 284 |
Signals from the real world Projects in signal processing | 293 |
Data compression | 294 |
Tour of lossless data compressors | 297 |
Sound | 307 |
Examples of sound compression | 314 |
Images | 317 |
Examples of image processing | 318 |
Image compression | 326 |
Support code for the book Projects | 331 |
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Common terms and phrases
algebra Appendix code applied approximation arithmetic asymptotic attractor bits Block Brownian Brownian noise Cantor set chaos complex compression computational constant continued fraction continuous wavelet transform convergence convolution Crandall curve DATA_TYPE Daubechies define difficulty level 1-3 digits discrete discrete wavelet transform double dragon curve encoding entropy error evaluation example factor fast algorithms fast wavelet transform Fermat number Figure formula Fourier transform fractal dimension giant Hermitian symmetry Implement initial integer interesting Investigate length Lyapunov exponents Mathematica matrix Mersenne Mersenne primes method mother function multiply NEXTSTEP number-theoretic transforms obtained optimal parameter pixels plot prime Print problem probs Project quadratic map random recursion register int Return Riemann Zeta function scheme sequence signal square step Support code symbol theoretical theory two-dimensional unsigned char vector void xeven xodd