Section 5.2  Introduction to the Phase Plane

• to be able to sketch trajectories and the direction field of a given system of differential equations
• to be able to determine integral curves
• to be able to convert second order equations into a first order system

• phase plane
• trajectory
• integral curves
• critical point
• equilibrium solution
• asymptotically stable
• unstable
• saddle point
• center
 

• finding critical point of a system, #3,10

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• determining integral curves, #7

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• solving phase plane equation and sketching trajectories,#11

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• understanding stability of critical points from the direction field in phase plane, #15

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• converting second order differential equation into a first order system, #19

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

SOLUTION.