By David Halpern, Howard B. Wilson, Louis H. Turcotte

Due to the fact its creation in 1984, MATLAB's ever-growing recognition and performance have secured its place as an industry-standard software program package deal. The undemanding, interactive setting of MATLAB 6.x, which incorporates a high-level programming language, flexible pictures features, and abundance of intrinsic capabilities, is helping clients concentrate on their purposes instead of on programming blunders. MATLAB has now leapt a long way sooner than FORTRAN because the software program of selection for engineering functions.

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**Additional resources for Advanced Mathematics and Mechanics Applications Using MATLAB**

**Example text**

Function linspace generates vectors % with equally spaced components. 1); axis(’square’); axis(rng); hold on 106: 107: 108: 109: 110: 111: 112: % Plot orthogonal grid lines which represent % the mapping of circles and radial lines x=real(w); y=imag(w); xo=real(wouter); yo=imag(wouter); plot(x,y,’-k’,x(1:end-1,:)’,y(1:end-1,:)’,... ’-k’,xo,yo,’-k’) 113: 114: 115: 116: 117: 118: % Add a title and axis labels title([’Mapping of a Square Using a ’, ... num2str(m),’-term Polynomial’]) xlabel(’x axis’); ylabel(’y axis’) figure(gcf); hold off; 119: 120: %============================================== 121: 122: 123: 124: 125: 126: 127: 128: 129: 130: function range=cubrange(xyz,ovrsiz) % % range=cubrange(xyz,ovrsiz) % ~~~~~~~~~~~~~~~~~~~~~~~~~~ % This function determines limits for a square % or cube shaped region for plotting data values % in the columns of array xyz to an undistorted % scale % © 2003 by CRC Press LLC 131: 132: 133: 134: 135: 136: 137: 138: 139: 140: 141: 142: 143: 144: 145: 146: 147: % xyz - a matrix of the form [x,y] or [x,y,z] % where x,y,z are vectors of coordinate % points % ovrsiz - a scale factor for increasing the % window size.

To assess the accuracy of the spline interpolation, values for ˆ −B ˆ approx ) and |(k − kapprox )/k| were obtained at 101 sample points along norm(B the curve. 15 show errors in the third decimal place except near the ends of the interpolation interval where a “not a knot” boundary condition is employed [27]. 15: Error Plot © 2003 by CRC Press LLC 100 120 Program Output and Code Program splinerr 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: function splinerr % Example: splinerr % ~~~~~~~~~~~~~~~~~ % % This program calculates the binormal and % curvature error for a spiral space curve.

User m functions called: % aspiral, crvprpsp crvprp3d cubrange splined %-------------------------------------------- 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: clear; hold off; clf; [R,T,N,B,KAP]=aspiral; m=size(R,2); [r,t,n,b,k]=crvprpsp(R,m); disp(’ ’); disp(... /KAP); hold off; clf; semilogy(1:m,errv,’k-’,1:m,errk,’k--’); xlabel(’point index’); ylabel(’error measure’); title(’Error Plot’); legend(’Binormal error’,’Curvature error’,3); figure(gcf); disp(’ ’) disp(’Press [Enter] to finish’); pause disp(’ ’), disp(’All done’), disp(’ ’) 26: 27: %============================================== 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: function [R,T,N,B,kap,tau,arclen]= ...

### Advanced Mathematics and Mechanics Applications Using MATLAB by David Halpern, Howard B. Wilson, Louis H. Turcotte

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