Unit IV: First-order Systems

Qualitative Behavior: Phase Portraits

« Previous | Next »

In this session we will leave off looking for exact solutions to constant coefficient systems of DE’s and focus on the qualitative features of the solutions. The main tool will be phase portraits, which are sketches of the trajectories of solutions in the xy-plane (now called the phase plane).

We will see that the qualitative nature of the solutions is determined by the eigenvalues of the coefficient matrix.

Session Activities

Read the course notes:

Watch the lecture video clips:

Read the course notes:

Learn from the Mathlet materials:

Watch the problem solving videos:

Complete the practice problems:

Check Yourself

Complete the problem sets:

« Previous | Next »

Course Info

Learning Resource Types

theaters Lecture Videos
theaters Recitation Videos
grading Exams with Solutions
laptop_windows Simulations
notes Lecture Notes
assignment_turned_in Problem Sets with Solutions