Vector Calculus II 23 (13 years)
Students predict from graphs of simple 2-d 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
- Dry-erasable plastic sleeves such as C-line CLI-40620.
- Copies of vector fields for the plastic sleeves.
- (Optional) Computers running Mathematica
- (Optional) The Mathematical notebook: How do we reference this??
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
- Learning Outcomes