MatlabNotes

14 Elementwise ExamplesExample 14.1 Draw graphs of the functionsi) y = sin xxii) u = 1(x 1)+ x 2iii) v = x2 +1x 2 4iv) w = (10 x)1/3 2(4 x 2 ) 1/2for 0 apple x apple 10.>> x = 0:0.1:10;>> y = sin(x)./x;>> subplot(221), plot(x,y), title(’(i)’)Warning: Divide by zero>> u = 1./(x-1).^2 + x;>> subplot(222),plot(x,u), title(’(ii)’)Warning: Divide by zero>> v = (x.^2+1)./(x.^2-4);>> subplot(223),plot(x,v),title(’(iii)’)Warning: Divide by zero>> w = ((10-x).^(1/3)-1)./sqrt(4-x.^2);Warning: Divide by zero>> subplot(224),plot(x,w),title(’(iv)’)Note the repeated use of the “dot” (elementwise)operators.Experiment by changing the axes (page 16),grids (page 12) and hold(page 13).>> subplot(222),axis([0 10 0 10])>> grid>> grid>> hold on>> plot(x,v,’--’), hold off,>> plot(x,y,’:’)Exercise 14.1 Tabulate the functionsandy =(x 2 + 3) sin ⇡x 2z =sin 2 ⇡x/(x 2 + 3)for x =0, 0.2,...,10. Hence, tabulate the functionw = (x2 + 3) sin ⇡x 2 sin 2 ⇡x(x 2 .+ 3)Plot a graph of w over the range 0 apple x apple 10.15 Two–Dimensional ArraysA rectangular array of numbers having m rowsand n columns is referred to as an m ⇥ n matrix.It is usual in a mathematical setting toenclose such objects in either round or squarebrackets—Matlab insists on square ones. Forexample, when m =2,n =3wehavea2⇥ 3matrix such asapple 5 7 9A =1 3 7To enter such an matrix into Matlab we typeit in row by row using the same syntax as forvectors:>> A = [5 7 91 -3 -7]A =5 7 91 -3 -7Rows may be separated by semi-colons ratherthan a new line:>> B = [-1 2 5; 9 0 5]B =-1 2 59 0 5>> C = [0, 1; 3, -2; 4, 2]C =0 13 -24 2>> D = [1:5; 6:10; 11:2:20]D =1 2 3 4 56 7 8 9 1011 13 15 17 1917