# New PDF release: A Bohr-Langmuir Transformatio

By Evans G. C.

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Fit’,... ’Interpolation Points’,1) title([’LEAST SQUARE POLY. AND POLY. ’,... 4 Conformal Mapping Example This example involves analytic functions and conformal mapping. (4k + 1) ∞ , bk = 1 k=0 and c is a scaling coefÞcient chosen to make z = 1 map to w = 1 (see reference [75]). Truncating the series after some Þnite number of terms, say m, produces an approximate square with rounded corners. Increasing m reduces the corner rounding but convergence is rather slow so that using even a thousand terms still gives perceptible inaccuracy.

The program reads the wave speed, the string length, and data points specifying the initial deßection. The solution is evaluated for a range of x, t values. 10, which is a three-dimensional plot of traces of the string deßection for a sequence of times. 33. 25. Finally, a function to animate the solution over two motion cycles illustrates how the initial deßection splits, translates, and reßects from the boundaries. 13: Motion Trace Over a Short Time Interval © 2003 by CRC Press LLC MATLAB Example Program strngrun 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: function strngrun(rundemo) % % strngrun(rundemo) % ~~~~~~~~~~~~~~~~ % This function illustrates propagation of % waves in a tightly stretched string having % given initial deflection.

Line 12,17,21 27 27,28,34-37 38 45,57 52,64 Operation several inline functions are deÞned function linspace generates vector of equidistant points inline functions called intrinsic spline function is used graph legends created graph images saved to Þles Program polyplot 1: 2: 3: 4: 5: 6: 7: 8: 9: function polyplot % Example: polyplot % ~~~~~~~~~~~~~~~~~~ % This program illustrates polynomial and % spline interpolation methods applied to % approximate the function 1/(1+x^2). % % User inline functions used: % cbp, Ylsq, yexact 10: 11: 12: 13: % Function for Chebyshev data points cbp=inline([’(a+b)/2+(a-b)/2*cos(pi/n*’,...