close all
clear all

figure(1);
x_vect = -5:.05:5;
[x,y] = meshgrid(x_vect,x_vect);
z = min(max(real(exp(x+sqrt(-1).*y)),-1000),1000);
h=surf(x_vect,x_vect,z);
%view(-42,83);
set(h,'FaceColor',[1 0 0]);
set(h,'FaceLighting','gouraud');
light('Position',[-2,2,20])
set(h,'EdgeColor','none')
xlabel('Realteil');
ylabel('Imaginärteil');
title('Die komplexe exp-Funktion, Re exp(z)')

figure(2);
x_vect = -0.5:.005:0.5;
[x,y] = meshgrid(x_vect,x_vect);
z = min(max(real(exp(1./(x+sqrt(-1).*y))),-100),100);
h=surf(x_vect,x_vect,z);
% view(-140,89);
set(h,'FaceColor',[1 0 0]);
set(h,'FaceLighting','gouraud');
light('Position',[-2,2,20])
set(h,'EdgeColor','none')
xlabel('Realteil');
ylabel('Imaginärteil');
title('Eine wesentliche Singularität')

figure(3);
x_vect = -5:.05:5;
[x,y] = meshgrid(x_vect,x_vect);
z = x+sqrt(-1).*y;
f = min(max(abs(1./(1+z.^2)),-3),3);
h=surf(x_vect,x_vect,f);
view(69,19);
set(h,'FaceColor',[1 0 0]);
set(h,'FaceLighting','gouraud');
light('Position',[-2,2,20])
set(h,'EdgeColor','none')
xlabel('Realteil');
ylabel('Imaginärteil');
title('Der Betrag von 1/(1+z^2)')


figure(4);
x_vect = -5:.05:5;
[x,y] = meshgrid(x_vect,x_vect);
z = x+sqrt(-1).*y;
f = min(max(real(log(z)),-5),5);
h=surf(x_vect,x_vect,f);
view(69,19);
set(h,'FaceColor',[1 0 0]);
set(h,'FaceLighting','gouraud');
light('Position',[-2,2,20])
set(h,'EdgeColor','none')
xlabel('Realteil');
ylabel('Imaginärteil');
title('Der Realteil des Logarithmus')

figure(5);
x_vect = -5:.05:5;
[x,y] = meshgrid(x_vect,x_vect);
z = x+sqrt(-1).*y;
f = min(max(imag(log(z)),-5),5);
h=surf(x_vect,x_vect,f);
view(69,19);
set(h,'FaceColor',[1 0 0]);
set(h,'FaceLighting','gouraud');
light('Position',[-2,2,20])
set(h,'EdgeColor','none')
xlabel('Realteil');
ylabel('Imaginärteil');
title('Der Imaginärteil des Logarithmus')




figure(5);
figure(4);
figure(3);
figure(2);
figure(1);