Green's Theorem

Green's Theorem is a fundamental result in calculus that relates the circulation of a vector field around a closed curve to the behavior of the field inside the region it encloses. In simple terms, it states that the total "twisting" or "rotation" of a field along the boundary equals the sum of the "twisting" happening within the area. This helps us convert complex calculations around a boundary into simpler calculations over the entire area, or vice versa, which is useful in physics, engineering, and fluid dynamics for analyzing flows and forces.