Vector fields and their flows

Learning objectives

  • Interpret functions f: {\bf R}^2 \longrightarrow {\bf R}^2 as vector fields in the plane
  • Use Mathematica to survey basic linear vector fields: sources, sinks, circles, spirals
  • Sketch flowlines (streamlines) of a vector field
  • Use Euler’s method to approximate a flowline.
  • Write the differential equation satisfied by streamlines of a vector field

Before class

  • Read Hughes-Hallett sections 7.3, 17.4
  • Ponder Hughes-Hallett problems: 17.3: 1-6, 7, 11, 13, 17; 17.4: 4, 10, 15.
  • Remember to bring your laptop to class