# Divergence & Stokes' Theorems

Canonical: https://manyspace.aporia.systems/topics/divergence-stokes-theorems-mth-multc-184
Updated: 2026-10-13

Mathematics · Multivariable Calculus · MTH-MULTC-184

- Difficulty: 3 / 5
- Importance: 5 / 5
- Study time: 3–6 h

Gauss divergence theorem, applications, physical meaning

## Why it matters

The global-to-local dictionaries of vector calculus; shape how EM and fluids are written.

## Where it is used

Writing Maxwell's equations in differential form; fluid circulation and flux.

## How you know you have learned it

Complete 3 independent examples correctly + explain common failure modes.

## What you need first

- [Surface Integrals](https://manyspace.aporia.systems/topics/surface-integrals-mth-multc-183) (required)
- [Integration by Parts](https://manyspace.aporia.systems/topics/integration-by-parts-mth-calc2-140) (required)
- [Green's Theorem](https://manyspace.aporia.systems/topics/green-s-theorem-mth-multc-182) (required)
- [Gaussian Elimination](https://manyspace.aporia.systems/topics/gaussian-elimination-mth-linalg-155) (helpful)

## What it opens

- [Maxwell's Equations](https://manyspace.aporia.systems/topics/maxwell-s-equations-phy-eandm-066)

## Resources

- Thomas' Calculus — Hass, Heil & Weir
- Calculus: Early Transcendentals — James Stewart
- Calculus: Early Transcendentals — James Stewart