1-forms, 2-forms, exterior derivative, and Stokes theorem
1-Forms
2-Forms
Stokes' Theorem
Exterior Derivative
ω = P dx + Q dy | ∫_C ω = ∫_a^b [P(c(t))c'₁(t) + Q(c(t))c'₂(t)] dt
A 1-form ω = P dx + Q dy is an oriented measurement device: it measures how much a path
"aligns" with its direction at each point. Exact forms (ω = df) have path-independent integrals.
The angle form has winding number 1 around the origin — it's closed but not exact on ℝ²\{0}.