Page 62 - Applied Numerical Methods Using MATLAB

PROBLEMS 51
>>x1 = [0:0.01:pi/2-0.01]; x2 = [pi/2+0.01:0.01:3*pi/2-0.01];
>>x3 = [3*pi/2+0.01:0.01:2*pi];
>>y1 = tan(x1); y2 = tan(x2); y3 = tan(x3);
>>subplot(222), plot(x1,y1,x2,y2,x3,y3), axis([0 6.3 -10 10])

(d) Try adjusting the number of intermediate points within the plotting
interval as follows.

>>x1 = [0:200]*pi/100; y1 = tan(x1);
>>x2 = [0:400]*pi/200; y2 = tan(x2);
>>subplot(223), plot(x1,y1), axis([0 6.3 -10 10])
>>subplot(224), plot(x2,y2), axis([0 6.3 -10 10])
From the difference between the two graphs you got, you might have
guessed that it would be helpful to increase the number of intermediate
points. Do you still have the same idea even after you adjust the range
of the y-axis to [−50, +50] by using the following command?

>>axis([0 6.3 -50 50])

(e) How about trying the easy plotting command ezplot()? Does it answer
your desire?

>>ezplot(’tan(x)’,0,2*pi)
1.6 Plotting the Graph of a Sinc Function
The sinc function is defined as

sin x
f(x) = (P1.6.1)
x
whose value at x = 0is

sin x (sin x)
f(0) = lim = = cos x = 1 (P1.6.2)
x→0 x x 1 x=0
x=0
We are going to plot the graph of this function over [−4π, +4π].
(a) Casually, you may try as follows.

>>x = [-100:100]*pi/25; y = sin(x)./x;
>>plot(x,y), axis([-15 15 -0.4 1.2])

In spite of the warning message about ‘division-by-zero’, you may
somehow get a graph. But, is there anything odd about the graph?
(b) How about trying with a different domain vector?

>>x = [-4*pi:0.1:+4*pi]; y = sin(x)./x;
>>plot(x,y), axis([-15 15 -0.4 1.2])