Discussion 12: Critical Points of Vector Fields

This discussion is a computer laboratory which requires access to Maple. The goal of this discussion is to understand the classification of critical points of a vector field as stable and unstable. This laboratory assumes that the students have completed Discussion 11 and are familiar with Maple worksheets and Maple syntax. This will be the first time that the students will have used the computer to plot vector fields and flow lines of vector fields.

The students are given six vector fields to analyze. They must locate the critical points and use the Maple commands fieldplot and DEplot to plot the vector fields and their flow lines. By the end of the laboratory session, the students should have developed a facility with the vector field and flow line plotting commands, so that they can describe and analyze the behavior of a vector field in the neighborhood of a critical point. These skills will be used extensively in Discussion 13. The computer portion of the laboratory should be completed in one class period. A lecture summarizing the results of this discussion, Discussion 11 and Section 2.4 should follow.