clc
echo on
% Example 1
% This is a script
% Executing a script is the same as typing the
% commands in the command window.
%
% The percent indicates the beginning of a comment
%
% MATLAB can do routine calculations
2+2

sqrt(2)

pause
clc
% MATLAB can use variables
% The equals sign indicates assignment
s = ans

t = s*s

u = exp(t)

pause
clc
% MATLAB can do complex arithmetic
s = sqrt(-2)

t = s*s

% and it knows Euler's formula
u = exp(s)
cos(imag(s))+i*sin(imag(s))
v = log(u)
pause
clc
% MATLAB is designed to work with vectors, 
% matrices, and arrays.

x = [1; 2; 3]

A = [1 1 1; 2 3 4; 0 1 -1]

y = A*x

pause
clc
% Unless otherwise indicated, arrays are 
% treated as matrices.  

A

A^2
% Use a period in front of the operator
% to shift to an array interpretation
A.^2
pause
clc

% MATLAB has loops and case statements

k = 1;
while k<3
    if mod(k,2)==0
        display('k is even')
    else
        display('k is odd')
    end
    k = k+1
end
        
pause
echo on
clc
% Plotting is so easy in MATLAB it gets a STAR
theta = 4*pi/5
echo off
for k=0:5
    z(k+1) = i*exp(i*k*theta);
end
plot(z)
        
echo off