Unit 17: Spreading and spinning: divergence and curl
About this unit
Divergence measures how much a flow spreads out from each point and curl how much it spins there, and both come from partial derivatives of the field's components.
By the end, you can: Read a 2D vector field as a flow, and compute and interpret divergence (net outflow: sources and sinks) and curl (local spin) from its components.
Modules
5 modulesLearn
- Spreading out: divergenceArticle · A vector field as a flow; divergence ∂P/∂x + ∂Q/∂y is the net outflow from a tiny region: positive at sources, negative at sinks; (x, y) has divergence 2.Not started
- Spinning: curlArticle · Curl ∂Q/∂x − ∂P/∂y is how fast a tiny paddle wheel turns: (−y, x) has curl 2; a shear flow (y, 0) has straight arrows but curl −1.Not started
- Find where the flow balancesExperiment · Move the probe in F = (x², y) to where the divergence 2x + 1 is zero, and see sources on one side and sinks on the other.Not started
- Divergence and curl in briefReview · The two formulas, what their signs mean, and the common mistakes.Not started