# 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