This 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.
Inhaltsverzeichnis
1 Numbers everywhere Selected topics in numerical analysis. - 1. 1 Numerical evaluation. - 1. 2 Equation solving. - 1. 3 Random numbers and Monte Carlo. - 2 Exploratory computation Collected intra- and interdisciplinary projects. - 2. 1 Mathematical problems. - 2. 2 Nature-motivated models. - 2. 3 Projects from biology. - 2. 4 Projects from physics and chemistry. - 3 The lure of large numbers Projects in number theory. - 3. 1 Large-integer arithmetic. - 3. 2 Prime numbers. - 3. 3 Fast algorithms. - 3. 4 Factoring. - 4 The FFT forest-The ubiquitous FFT and its relatives. - 4. 1 Discrete Fourier transform. - 4. 2 FFT algorithms. - 4. 3 Real-valued transforms. - 4. 4 Number-theoretic transforms. - 5 Wavelets Young arrivals in the transform family. - 5. 1 Chords, notes, and little waves. - 5. 2 Discrete wavelet bases. - 5. 3 Discrete wavelet transform. - 6 Complexity reigns Chaos & fractals & such. - 6. 1 Chaos. - 6. 2 Fractals. - 7 Signals from the real world Projects in signal processing. - 7. 1 Data compression. - 7. 2 Sound. - 7. 3 Images. - Appendix Support code for the book Projects. - References.
