%% MATLAB Short Course 4: MATLAB functions and solving differential equations

%% get the complex square z+iw = (x+iy)^2 =x^2-y^2+2xyi
%function [z,w] = myfun3(x,y)
%% z + iw = (x+iy)^2 = x^2-y^2 + 2ixy
%z = x^2 - y^2;
%w = 2*x*y;
[z, w] = myfun3(1,1)

%% only the first output is displayed
myfun3(1,1) % only z is displayed

%% Solve the ODE y' = -y^3+sin(t)

% define it as a simple anonymous function
myode1 = @(t,y) -y^3+sin(t);
% call the generic solver "ode45"
[t,y] = ode45(myode1,[0,3],-1);
plot(t,y)

%% Solve the more complicated Lorenz ODEs
[t,Y] = ode45(@(t,y)lorenzode(t,y),[0 50],[1 0 0]);
% Y is a large matrix with three columns (three variables)
plot3(Y(:,1),Y(:,2),Y(:,3))