Green's Theorem: Understanding Rotations and Closed Paths

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Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Green's Theorem: Applications

Covers the application of Green's Theorem in analyzing vector fields and calculating line integrals.

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Differential Forms Integration

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

Surface Integrals, Divergence Theorem and Stocks' Theorem

Covers surface integrals, the divergence theorem, and Stocks' theorem through examples and analogies.

Harmonic Forms: Main Theorem

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

Surface Integrals, Divergence Theorem

Covers surface integrals, divergence theorem, and regular domains in 2D and 3D.