Describing How Fields Behave

Divergence and curl give us tools to describe how vector fields spread out or twist. They're central concepts in understanding the behavior of physical fields.

• Divergence measures how much a vector field spreads out from a point (like water gushing from a spring).
• Curl measures how much a vector field rotates around a point (like a whirlpool).

The Big Theorems

• Green's Theorem connects line integrals around a closed curve to double integrals over the region inside.
• Stokes' Theorem generalizes Green's Theorem to surfaces in 3D.
• Divergence Theorem relates the flow out of a volume to the behavior on its boundary.

These theorems make hard calculations easier and reveal deep connections between local and global properties of fields.

Why Do They Matter?

They're fundamental in physics for understanding electromagnetism, fluid dynamics, and more.