Visualizing Curl

Highlights of the activity

1. This computer visualization activity is designed to provide students with a geometric understanding of curl.
2. Students use Maple/Mathematica and the definition of curl as circulation per unit area to learn how to estimate the value of the curl at any point for a variety of vector fields.
3. Discussion focuses on choosing an area that respects the symmetry of the field and on considering the curl at many different points.

Reasons to spend class time on the activity

The traditional discussion of curl in vector calculus derives an algebraic expression in rectangular coordinates. We prefer to give a geometric derivation as circulation per unit area around an appropriately shaped closed curve. This worksheet helps students learn how to predict the value of the curl at any point by looking at the vector field near that point.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Maple Worksheet

vfcurlvis.mw (Maple 13)

vfcurlvis.mws (Maple 11 Classic)

Mathematica Notebook

vfcurlvis.nb