% Last update: 03/05/04

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%MATLAB COMMAND                 EXPLANATION (by Luis Carvalho)
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% general 

>> clear			% clear variables (if any)
>> f = inline('(3*x - y)/2')	% define a function f(x)
>> f(0,1)			% evaluate f at x=0 and y=1 (f(0,1)=-0.5)
>> pi				% the number 3.1415... .
>> exp(2.5)			% exponential function evaluated at 2.5
>> ln(2.5)			% the natural logarithm of 2.5
>> x = 1 + 2 + 3 + 4 + 5 + ...	% if the expression is long
	6 + 7 + 8 + 9 + 10	% you can break the lines using "..."
>> p = 'x^2 + 2*x'		% store the expression x^2+2*x (as a string)
				% under the name "p"

% plotting functions and points

>> p = inline('x.^2 + 2.*x')	% we can now use p as a function
>> x = 0:0.1:1			% x = [0, 0.1, 0.2, ..., 0.9, 1], a vector
>> x(2)				% second position in x, x(2) = 0.1
>> y = p(x)			% y = [p(0), p(0.1), p(0.2), ..., p(1)]
				% y is a vector with the same size as x
>> length(y)			% the size (# of entries) of y: 11
>> plot(x, y, 'b-')		% plot x against y, using a blue (b) line (-)
>> y2 = y			% y2 is a copy of y
>> y2(3) = 1			% change the third entry of y2 to 1
>> plot(x, y2, 'r*')		% plot x against y2 using red (r) starts (*)
>> plot(x, y, 'b-', x, y2, 'r*')% plot x against y and y2
>> hold on			% you can also use "hold on" to pile up plots
>> plot(x, y, 'ko')		% plot y now in black (k) circles (o)
>> plot(x, y2, 'g.')		% and y2 in green (g) dots (.)
>> hold off			% quit holding

% solving equations

>> solve('cos(x) + y = 9', 'x')	% solve an equation for x
>> [x, y] = solve('x^2 * y^2 = 0', ...	'x - y = 1')	
				% solve a system of equations
				% and store results in x and y
>> fsolve('x.^3 - 2.*x + 1, [-1, 1])	
				% numerically solve x^3 - 2*x + 1 = 0
				% for x between -1 and 1

%% differential equations

>> dsolve('Dx = 3*x*(1-x/300)')	% solve the ODE dx/dt = 3*x*(1-x/300). Note that
				% "D" denotes differentiation with respect to "t"
>> diffeq = 'Dx = 3*x*(1-x/300)'% use variables to get shorter commands
>> dsolve(diffeq, 'x(0) = 50')	% now we have an IVP
>> y = dsolve('D2y = sin(y)')	% you can also specify second order ODEs...
>> x = dsolve('D3x = -x', ...'x(0)=1, Dx(0)=0, D2x(0)=0')	
				% ... higher order IVPs
>> ezplot(x)			% and plot them