Geometry of Flows of First-Order ODEs: Vector Fields (More Complex Example)

Slightly more complicated example: = y sin(),
(dt,dy) = dt(1,ysin))

As in the simpler example above we first plot the derivative's value as a surface using Plot3D, then we represent the behavior as a vector field

To summarize this part, we have seen how first-order differential equations have associated trajectories in the plane of the dependent variables, analogous to what we simulated above by incrementing a certain functional relationship. Numerical differential equation solvers use similar techniques.

Created by Wolfram Mathematica 6.0  (06 November 2007)