% Matlab diary from cs110a, Feb 25 2005.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

help ode23tx
help ode45
clc
edit f
type f

function ydot = f(t,y)
% F  :  function ydot = f(t,y) for ODE solution
%
%   t:  scalar time
%   y:  vector, y = y(t), unknown function
%   
%   ydot:  vector of dy / dt
ydot = y/2;

ode45( @f, [0 10], 1);
ode45( @f, [0 10], 1);title('y(t) defined by ydot=f(t,y)'); xlabel('t'); ylabel('y');
exp(5)
g = inline('y/2', 't', 'y')
f(1,1)
g(1,1)
ode45( g, [0 10], 1);title('y(t) defined by ydot=g(t,y)'); xlabel('t'); ylabel('y');
h = @(t,y) y/2
h(1,1)
ode45( h, [0 10], 1);title('y(t) defined by ydot=h(t,y)'); xlabel('t'); ylabel('y');
exp(5)
ans =
  148.4132
clc
opts = odeset('reltol',10^-6);
opts
ode45( h, [0 10], 1, opts);title('y(t) defined by ydot=h(t,y)'); xlabel('t'); ylabel('y');
clc
edit f
type f

function ydot = f(t,y)
% F  :  function ydot = f(t,y) for ODE solution
%
%   t:  scalar time
%   y:  vector, y = y(t), unknown function
%   
%   ydot:  vector of dy / dt
ydot = -y/2;

ode45( @f, [0 10], 1);title('y(t) defined by ydot=f(t,y)'); xlabel('t'); ylabel('y');
edit f
type f

function ydot = f(t,y)
% F  :  function ydot = f(t,y) for ODE solution
%
%   t:  scalar time
%   y:  vector, y = y(t), unknown function
%   
%   ydot:  vector of dy / dt
ydot = t;

ode45( @f, [0 10], 1);title('y(t) defined by ydot=f(t,y)'); xlabel('t'); ylabel('y');
clc

edit lve
type lve

n ydot = lve(t,y)
% LVE :  ydot as a function  of t and y(t) for Lotka-Volterra eqns
%
% t : time
% y : vector y = [rabbits(t) ; foxes(t)]
alpha = .01;
ydot = [ 2*y(1) - alpha * y(1)*y(2)  ;   -y(2) + alpha*y(1)*y(2) ];

lve(2,[3 ; 4])
ans =
    5.8800
   -3.8800
clc
ode45( @lve, [0 20], [300 ; 150]);
legend('rabbits','foxes')
ode45( @lve, [0 20], [15; 22]);
legend('rabbits','foxes')
ode45( @lve, [0 20], [102, 198]);
legend('rabbits','foxes')
ode45( @lve, [0 20], [100, 200]);
legend('rabbits','foxes')