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Projects in Scientific Computation
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Table of Contents

1 Numbers everywhere Selected topics in numerical analysis.- 1.1 Numerical evaluation.- 1.1.1 Evaluation of famous constants.- 1.1.2 Evaluation of elementary functions.- 1.1.3 Special functions.- 1.2 Equation solving.- 1.2.1 Matrix algebra.- 1.2.2 Non-linear equation systems.- 1.2.3 Differential equations.- 1.3 Random numbers and Monte Carlo.- 1.3.1 Generating Random Numbers.- 1.3.2 Numerical integration and Monte Carlo.- 2 Exploratory computation Collected intra- and interdisciplinary projects.- 2.1 Mathematical problems.- 2.1.1 Planar geometry problems.- 2.1.2 Symbolic manipulation.- 2.1.3 Real and complex analysis.- 2.2 Nature-motivated models.- 2.2.1 Neural network experiments.- 2.2.2 Genetic algorithms and artificial life.- 2.3 Projects from biology.- 2.3.1 Population models.- 2.3.2 Physiology, neurobiology, and medicine.- 2.3.3 Molecular biology.- 2.4 Projects from physics and chemistry.- 2.4.1 Classical physics.- 2.4.2 Quantum theory.- 2.4.3 Molecules and structure.- 2.4.4 Relativity.- 3 The lure of large numbers Projects in number theory.- 3.1 Large-integer arithmetic.- 3.1.1 Testing the operations.- 3.2 Prime numbers.- 3.2.1 Mersenne primes.- 3.2.2 Primes in general.- 3.3 Fast algorithms.- 3.3.1 Fast multiplication.- 3.3.2 Fast mod, division, inversion.- 3.3.3 Other fast algorithms.- 3.4 Factoring.- 3.4.1 Factoring algorithms.- 3.4.2 Status of Fermat numbers.- 4 The FFT forest-The ubiquitous FFT and its relatives.- 4.1 Discrete Fourier transform.- 4.1.1 Fundamental DFT manipulations.- 4.1.2 Algebraic aspects of the DFT.- 4.1.3 DFT test signals.- 4.1.4 Direct DFT software.- 4.2 FFT algorithms.- 4.2.1 Recursive FFTs.- 4.2.2 FFT indexing and butterflies.- 4.2.3 Complex FFTs, N a power of 2.- 4.2.4 Real-signal FFTs.- 4.2.5 FFTs for other radices.- 4.2.6 FFTs in higher dimensions.- 4.2.7 Applications of the FFT.- 4.3 Real-valued transforms.- 4.3.1 Hartley transform.- 4.3.2 Discrete cosine transform.- 4.3.3 Walsh-Hadamard transform.- 4.3.4 Square-wave transform.- 4.4 Number-theoretic transforms.- 4.4.1 Exploring number-theoretic transforms.- 5 Wavelets Young arrivals in the transform family.- 5.1 Chords, notes, and little waves.- 5.1.1 Windowed Fourier transform.- 5.1.2 Continuous wavelet transform.- 5.2 Discrete wavelet bases.- 5.2.1 Example wavelet expansions.- 5.2.2 Mother function and its wavelet.- 5.2.3 Wavelets of compact support.- 5.3 Discrete wavelet transform.- 5.3.1 Fast wavelet transform algorithms.- 5.3.2 Applications of fast wavelet transforms.- 6 Complexity reigns Chaos & fractals & such.- 6.1 Chaos.- 6.1.1 Quadratic map algebra.- 6.1.2 Bifurcation and chaos.- 6.1.3 Chaos models.- 6.1.4 Chaos, stability, and Lyapunov exponents.- 6.1.5 Applications of chaos theory.- 6.2 Fractals.- 6.2.1 Theory of fractals.- 6.2.2 Visualization of fractals.- 6.2.3 Fractal Brownian noise.- 6.2.4 Measurement of fractal dimension.- 7 Signals from the real world Projects in signal processing.- 7.1 Data compression.- 7.1.1 Tour of lossless data compressors.- 7.2 Sound.- 7.2.1 Examples of sound processing.- 7.2.2 Examples of sound compression.- 7.3 Images.- 7.3.1 Examples of image processing.- 7.3.2 Image compression.- Appendix Support code for the book Projects.- References.

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