To find the definite integral of a function:
> integrate(sqrt(1-x^2),x=0..1);
To graph a function:
> plot(sin(1/x),x=0..1);
To plot the slope field for a differential equation:
> DEplot(diff(T(t),t)=0.1*(400-T),T(t),t=0..30,T=0..500);
or:
> DEplot(diff(y(x),x)=1/(x^2-1),y(x),x=-2..2,y=-2..2);
or:
> DEplot(diff(p(t),t)=-p*(p-2.5),p(t),t=0..5,p=0..5);
Never mind the man behind the curtain:
> DEplot3d( {diff(x(t),t)=-.10*x(t)+0.05*z(t),
diff(y(t),t)=-0.1*y(t)+0.1*x(t), diff(z(t),t)=-0.1*z(t)+0.1*y(t)} , [x(t),
y(t), z(t)], t=0..180, [[x(0) = 10, y(0) = 0, z(0)= 0]], stepsize=0.1);
To plot a function in polar coordinates:
> with(plots):
> polarplot(cos(3*t),t=0..2*Pi);