Calc III Lab: Nodes
The phase portraits you will see in this section of the lab are called
nodes. As was the case for the focus equilibria,
the equilibrium in the phase portrait for a node is
referred to as a "sink" or a "source," depending on whether or not it is
locally attracting.
Activity
Compute solutions to the linear differential equation determined by
the matrix with entries
(a,b,c,d)=(-1,-1,0.125,0).
- Clear the old phase portrait.
- Compute the phase portrait for this system.
- Compute the trace and determinant of the associated matrix.
- Plot the ordered pair (det, trace) on the diagram provided.
- Sketch the phase portrait (with arrows!) on the diagram.
- Indicate any straight-line solutions, or write "No straight-line
solutions" on your sketch.
- Do the same for the linear differential equation determined by
the matrix with entries
(a,b,c,d)=(1,-1,0.125,0).
Go To
Robert E. Thurman <thurman@geom.umn.edu>
Last modified: Mon Nov 18 13:32:46 1996