Vector Calculus II 23 (13 years)
Students predict from graphs of simple 2d vector fields whether the divergence is positive, negative, or zero in various regions of the domain using the geometric definition of the divergence of a vector field at a point as flux per unit volume (here: area) through an infinitesimal box surrounding that point. Optionally, students can use computer algebra to verify their predictions.
 group Small Group Activity
schedule
30 min.
build
 Dryerasable plastic sleeves such as Cline CLI40620.
 Copies of vector fields for the plastic sleeves.
 (Optional) Computers running Mathematica
 (Optional) The Mathematical notebook: How do we reference this??
description Student handout (PDF)
What students learn
 Divergence of a vector field (at a point) is the flux per unit volume through an infinitesimal box.
 How to predict the sign and relative magnitude of the divergence from graphs of a vector field.
 (Optional) How to calculate the divergence of a vector field with computer algebra.
For each of the vector fields below, decide whether the divergence is postive, negative, or zero in each quadrant. Be prepared to defend your answers.
 Author Information
 Corinne Manogue
 Keywords
 Learning Outcomes
