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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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27

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Numerical methods

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27.1 Use an iteration procedure to find the root of the equation 40x = exp x to four significant figures.

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To provide a satisfactory iteration scheme, the equation must be rearranged in the form x = f(x), where f(x) is a slowly varying function of x; we then use xn+1 = f(xn) as the iteration scheme.

In the present case the rearrangement is straightforward, as, by taking logarithms, we can write the equation as x = ln 40x. Since ...

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