Partial Derivatives: Derivative of an Integral with Parameter-dependent Bounds

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores partial derivatives, continuity of functions, mean value theorem, and uniform continuity.

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Covers differentiability, derivatives, composite functions, linear approximation, and partial derivatives.