
Math 241 Maple Workshop 


San Diego State University  This page last updated 25Aug01 
Maple provides a powerful tool to visualize the solutions of differential equations and other objects in mathematics. Below is the classical example of a damped oscillator given by the differential equation:
y" + 0.4y' + y = 0
or the equivalent system of differential equations:
The Maple command for viewing the 3D solution is given by
> with(DEtools):
> DEplot3d({D(x)(t)=y(t), D(y)(t)=x(t)  0.4*y(t)}, [x(t),y(t)], t=0..10, [[x(0)=0,y(0)=1], [x(0)=0,y(0)=.5], [x(0)=0,y(0)=1], [x(0)=0,y(0)=.5], [x(0)=1,y(0)=0], [x(0)=0.5,y(0)=0], [x(0)=1,y(0)=0], [x(0)=0.5,y(0)=0]], scene=[t,x(t),y(t)], stepsize=.1, title=`Damped oscillations`, linecolour=tsqrt(t));
Below we show a shockwave flash movie with different viewing angles of this damped oscillator, including the 2D special views of time vs. position, time vs. velocity, and velocity vs. position (Phase portrait).