% ____________________________________________________________________
%  Nonlinear dynamics I: Chaos
%  
%  Supplementary code for Pset 1
% ____________________________________________________________________
% 
% The first part of the code plots a function y = f(x). 
% The second part of the code plots a trajectory of a particle, for which
% the two coordinates (x,y) are given as a function of time. 
%
% ____________________________________________________________________
%     Part I 
% ____________________________________________________________________
% objective: plot y = sin(x) and y = cos(x) for 0<=x <= pi, 
%           label the graphs, put in title, make lines thicker
%

clear all;  % clears all the values of the variables that you used before
close all;  % closes all the figure windows that you used before
clc;        % clears the command window screen

% make an array x (from 0 to pi with a step of 0.1)
x = 0:0.1:pi ;            

% open figure 42 (matlab enumerates figures, you can give them different
% numbers if you want several plots on different figures 
figure(42); 

% plot y = sin(x) in dots in red color
plot(x,sin(x),'.r'); 

% tell the figure to "hold on", otherwise when you plot the next graph it
% will erase the previous one
hold on; 

% plot y = cos(x) in dash-dot in blue
plot(x,cos(x),'-.b','LineWidth',4); 

% give anohter variable y the values of sin(x+0.2). It will be an array
% since x is an array
y = sin(x+0.2);

% in 2D plot y = f(x)
plot(x,y,'k');

% give labels to the x and y axes, put in a title in bigger font
xlabel x
ylabel y 
title('y = sin(x) and y = cos(x)','FontSize',20);

% if you don't use axis tight, MATLAB leaves some space on the left and
% right of the graph, so the x axis would be from -0.3 to 3.5
% (approximately) instead of 0 to pi. 
axis tight; 

% you can label all the graphs that you plotted
legend('y = sin(x)','y = cos(x)', 'y = sin(x + 0.2)');

% ____________________________________________________________________
%     Part II 
% ____________________________________________________________________
% objective: plot a trajectory of a particle, for which
% the two coordinates (x,y) are given as a function of time. 

t = 0:0.01:10;
x = sin(t); 
y = cos(t); 

figure(2); 
plot(x,y,'m','LineWidth',4); 
xlabel('x','FontSize',20); 
ylabel('y'); 
title('Trajectory of a particle','FontSize',24);
axis equal; grid on; 



% ____________________________________________________________________
%     Part III
% ____________________________________________________________________
% objective: how to look for help? Type help and then the name of the
% function that you want the description of. 

help plot3