Date 14.5.99
Student 45834H, Mikko Hämäläinen

Problem Set 4

Problem 1

File: h4t1.m



% Poisson kernel on the unit disc

x=0;
y=1;

r = [0:0.05:1];
theta = [0:2*pi/100:2*pi];

X = r'*cos(theta);
Y = r'*sin(theta);

n = 1 - X.^2 - Y.^2;
D = 2*pi*((X-x).^2 + (Y-y).^2);
z = n./D;

colormap(hsv);
surf(X,Y,z);
shading flat;

The Matlab code based on the lecture material...


Problem 2
File: h4t2.m 



% Harmonic functions on the unit disk

r=[0:0.05:1];
theta=[0:2*pi/100:2*pi];

X=r'*cos(theta);
Y=r'*sin(theta);

R=r'*ones(size(theta));
TH=ones(size(r'))*theta;

% Here is the degree n
n=4;

g=R.^n.*cos(n.*TH);
surf(X,Y,g);
colormap(copper);

... as the problem 1.