By Tao Pang

ISBN-10: 0521532760

ISBN-13: 9780521532761

Completely up to date and revised for its moment version, this complex textbook offers an advent to the fundamental tools of computational physics, and an summary of contemporary growth in different parts of medical computing. Tao Pang provides many step by step examples, together with application listings in JavaTM, of functional numerical tools from smooth physics and similar components. 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 is going to even be an invaluable reference for someone interested in computational study.

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3 The Millikan experiment Here we use a set of data from the famous oil drop experiment of Millikan as an example to illustrate how we can actually employ the least-squares approximation discussed above. Millikan (1910) published his famous work on the oil drop experiment in Science. Based on the measurements of the charges carried by all the oil drops, Millikan concluded that the charge carried by any object is a multiple (with a sign) of a fundamental charge, the charge of an electron (for negative charges) or the charge of a proton (for positive charges).

The accuracy of the linear interpolation can be improved by reducing the interval h i = xi+1 − xi . However, this is not always practical. Let us take f (x) = sin x as an illustrative example here. 000. 854 from Eq. 1). 924. 070, which is smaller than the maximum error estimated with Eq. 077. The above example is a very simple one, showing how most interpolation schemes work. A continuous curve (a straight line in the above example) is constructed from the given discrete set of data and then the interpolated value is read off from the curve.

J−1 + f i+1... 13) with f i = f (xi ) to start. 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.

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