Lectures related to Curve Integrals: Gauss/Green Theorem

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Residue Theorem: Calculating Integrals on Closed Curves

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

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Graph Surfaces: Integration and Vector Calculus

Covers integrating functions over graph surfaces in vector calculus, emphasizing the interpretation of divergence theorem and special cases of domain between two graphs.

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Harmonic Forms: Main Theorem

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

Geometric Meaning of Line Integrals

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

Stokes Theorem

Covers the Stokes theorem, extending the Green theorem to surfaces in R3 and explaining its application.