Homework #13

15.17

Matlab:

w1 = 2;

w2 = 2;

L = @(th,al) w1./sind(th)+w2./sind(180-al-th);

hold off;

L_thmin = [];

for al = [45:135],

th = [10:179-135];

plot(th,L(th,al));

hold on;

[lm,Lin] = min(L(th,al))

L_thmin = [L_thmin,min(L(th(Lin),al))];

end

hold off

plot((45:135),L_thmin);

16.32

For this problem the derivative was taken for the function then the value was places back in the original value to find the maximum.

Matlab:

e_0 = .85e-12;

q = 2e-5;

a = 0.9;

x = (0:0.001:15);

Q = q;

c1 = 1/(4*pi^e_0) *(q*Q);

F =@(x) c1*x./(x.^2+a.^2).^(3/2);

hold off;

plot (x,F(x));

hold on;

plot (a/sqrt(2), F(a/sqrt(2)), '*r');

16.25

The solution can be found at 1,3 based on using the max function in matlab.

Matlab:

s = (0:0.001:10);

T =@(s) 15* (s-s.^2)./((1-s).*(4*s.^2-3*s+4));

hold off

plot (s,T(s));

ess = rand(1,100000) *10;

[y,i] = max(T(ess));

hold on

plot (ess(i),y,'r*');