Vector Calculus: Green's Theorem

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Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

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 Theorem: Applications

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

Curve Integrals: Gauss/Green Theorem

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

Green's Theorem: Boundary and Normal Vectors

Explores boundaries, normal vectors, and Green's theorem application in transforming integrals.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Green's Theorem: Transforming Integrals in 2D

Covers Green's Theorem, transforming 2D integrals into 1D line integrals.

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

Vectorial Fields: Parametrization and Stokes' Theorem

Covers the parametrization of vectorial fields and the application of Stokes' theorem.

Divergence and Stokes' Theorems

Introduces the divergence and Stokes' theorems, comparing surface and volume integrals, and explains parameterization of surfaces and boundaries.