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36 pages, January 14, 2008,

Abstract:

Contents: numerics, matrices, FFT, ODEs computations, fitting data, Finite difference methods, simulated "annealing", wave propagation, List of figures A quote from author's statement that sums up the exposition: "Numerical, or computational physics is a branch of physics with an age-old tradition. If you can't produce a number, you have achieved nothing says (Richard) Feynman (Nobel Laureate in Physics, in QED) ,and right he is. More often than not this is possible only by computing. This series of lectures introduces standard methods of computational physics. The computational power which is available to the average student or researcher has grown by a factor of thousand or so, within the last twenty years. And with it the availability of high quality software. Therefore, these lectures concentrate on how to use software, and not how to develop it. Quite naturally, this boils down to MATLAB.This series of lectures is about standard numerical techniques for computing in physics. Although teachers prefer examples which can be solved by pencil and paper, or by chalk on the blackboard, most problems cannot be solved analytically. They require computations. Computational physics has a long tradition. However, computational physics cannot be taught any more in the traditional way. In 1980, the first IBM personal computer could address 64 kB of memory, its mass storage was a oppy of 360 kB, and it ran at 8 MHz with an 8 bit processor. For 15,000 EUR (about30,000) it was 'cheap' as compared to mainframes. Today, an electronic computer, such as my laptop, costs 1500 EUR (about 2,500 USD). Its 32 bit processor runs at 1.2 GHz, is supported by 512 MB ( now minimum > 1.5 GB for $100) fast storage, 40 GB (now >1 TB for less than 200 USD) mass storage, ethernet and modem controller on board, and so forth. This amounts to a many hundred--fold increase in computational power within the last two decades. Moreover, high quality software to be run on these 'cheap and highly efficient' computers has become 'cheap' (inexpensive). Just study the price list of the MathWorks corporation for Matlab. Today, a course on computational physics, in particular an introduction, should concentrate on how to use available and cheap high quality software, and not how to develop it. I have decided on using Matlab for various reasons..." (Presenter's comment: Mathematica(TM) or Maple(TM) may also provide very competitive alternatives along with National Labs' s simulation software.) Free web downloads at: http://www.home.uni-osnabrueck.de/phertel/num/np.pdf "List of Figures: 1 The black body radiation spectral intensity S(x) where x =kBT 9 2 Planetary motion without explicite accuracy control p.13 3 Total energy vs. time without accuracy control p.13 4 Planetary motion with accuracy control p14 5 Noisy cosine (50 Hz) vs. time sampled at millisecond steps p16 6 Spectral power of noisy cosine vs. frequency (Hz) p17 7 Noisy quadratic relationship between x (abscissa) and y (ordinate) and reconstruction by quadratic regression p19 8 A Gaussian peak on top of background: signal (black), signal plus noise (blue dots) and reconstructed signal (red) p.20 9 The shortest itinerary found by the simulated annealing algorithm p23 10 Analytic solution (full line) and finite difference approximation (red) of f (00_ + f = 0 with f(0) = 0 and f(=2) = 1 (black) p. 26 11 The lowest order eigenmode of \sq u = u on an L-shaped domain has become their logo p28 12 Contour plot of u = u(t; x). Cranck-Nicolson scheme, 100 time propagation steps, t running from left to right. Initially, u(0; x) = sin(x) + sin(2x) 36". Very nice computer presentation of Laplace function solutions, and the hardware and software have become a lot more powerful and less expensive in the USA than cited by the EU author.

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Open access: http://www.home.uni-osnabrueck.de/phertel/num/np.pdf

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