Vector Calculus: Line Integrals

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Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Geometric Meaning of Line Integrals

Explores the geometric interpretation of line integrals in altimetric profiles of cycling stages.

Vectorial Fields: Parametrization and Stokes' Theorem

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

Surface Integrals, Divergence Theorem and Stocks' Theorem

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

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, energy calculations, potential functions, and tangential vectors, with a focus on line integrals and domains.

Parametric Curves and Derivatives

Explores parametric curves, derivatives, equivalence of paths, and local behavior of functions.

Green's Theorem: Applications

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

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.