Calculus › Section P · Vector analysis › Topic P.7
The divergence theorem
For a closed surface, the total outward flux of a vector field equals the integral of its divergence over the solid inside — a boundary measurement traded for an interior one.
In this topic
- The statement
- Why it is true: a sketch
- Worked example: the sphere, officially
- Worked example: a cube, checked six ways
- Zero flux without a zero field
- Solids with holes
- Where the theorem earns its keep
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP