Discussion 11: Vector Fields

The goal of this discussion is to develop a graphical understanding of the behavior of individual flow lines and the family of flow lines of a vector field. The discussion should be done before covering Section 2.4: Vector Fields, however before beginning this discussion, it will be necessary to introduce and motivate the definitions of a vector field and a flow line of a vector field. The discussion also relies on the material in Section 2.2 of the text, in particular, on the definition of the tangent vector of a parametric curve.

In the first exercise, students are asked to describe how they would sketch a flow line on the plot of a vector field. In the second exercise, they are given several plots of vector fields and are asked to sketch the family of flow lines on the plots, locate the critical points of the vector fields, and describe in words the behavior of the families of flow lines. Students should be able to complete this discussion in one class period.