Complex functions and flow around a cylinder part 1 (matlab). Full article available at: http://www.firsttimeprogrammer.blogspot.com/2015/07/complex-functions-and-flow-around.html

complex_flow1.m

% Set up
x = -4:0.2:4;
y1 = -4:0.2:4;
y = (-4:0.2:4)*1i;

[X, Y]= meshgrid(x,y);

% Complex variable s
s = X + Y;
% Complex function f(z)
z = s + 1./s;

%--------------------------------------------------------------------------
% Plot the surfaces (abs(), real() and imag())

%Absolute value
figure
subplot(1,3,1);
surfc(x,y1,abs(z));
xlabel('x');ylabel('y');zlabel('z');
title('Absolute value');

%Real part
subplot(1,3,2)
surfc(x,y1,real(z));
xlabel('x');ylabel('y');zlabel('z');
title('Real part');

%Imaginary part
subplot(1,3,3)
surfc(x,y1,imag(z));
xlabel('x');ylabel('y');zlabel('z');
title('Imaginary part');