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An Introduction to Computational Physics by Tao Pang

By Tao Pang

Completely up to date and revised for its moment version, this complicated textbook presents an advent to the fundamental tools of computational physics, and an outline of contemporary development in numerous parts of medical computing. Tao Pang offers many step by step examples, together with application listings in JavaTM, of useful numerical tools from sleek physics and comparable parts. Now together with many extra workouts, the amount can be utilized as a textbook for both undergraduate or first-year graduate classes on computational physics or medical computation. it's going to even be an invaluable reference for a person focused on computational study.

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For example, complete coverage of the issues involved in creating good random-number generators could form a separate book. Therefore, we only focus on the basics of the topics here. 1 Interpolation In numerical analysis, the results obtained from computations are always approximations of the desired quantities and in most cases are within some uncertainties. This is similar to experimental observations in physics. Every single physical quantity measured carries some experimental error. We constantly encounter situations in which we need to interpolate a set of discrete data points or to fit them to an adjustable curve.

If we want to obtain f (x) from a given set f i for i = 0, 1, . . , n, we can carry out n levels of consecutive linear interpolations as shown in Fig. 1. 223 891 linear interpolations of the adjacent values. 14) and f 01234 = x − x4 x − x0 f 0123 + f 1234 . 15) It can be shown that the consecutive linear interpolations outlined in Fig. 1 recover the standard Lagrange interpolation. The Aitken method also provides a way of estimating the error of the Lagrange interpolation. 16) where the differences are taken from the last two columns of the hierarchy.

The following method is an implementation of the exponential random-number generator given in the above equation and is constructed from a uniform random-number generator. // Method to generate an exponential random number from a // uniform random number in [0,1]. } The uniform random-number generator obtained earlier is used in this method. Note that when this method is used in a program, the seed still has to be a global variable. 81) where σ is the variance of the distribution, which we can take as 1 for the moment.

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