Lectures related to Curve Integrals: Gauss/Green Theorem

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

Vector Calculus Theorems

Explores the Gauss and Green theorems in vector calculus, showcasing their applications through practical examples and geometric interpretations.

Surface Integrals, Divergence Theorem and Stocks' Theorem

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

Improper Integrals: Convergence and Comparison

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

Green's Theorem: Understanding Rotations and Closed Paths

Explores Green's Theorem, rotations, closed paths, and integral signs.

Green's Theorem in 2D: Applications

Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.

Green's Theorem: Applications

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

Vector Calculus: Line Integrals

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

Understanding Positive and Negative Orientation in Curves

Explores positive and negative orientation in curves, emphasizing their impact on tangent and normal vectors.

Divergence Theorem: Green Identities in R²

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

Vectorial Fields: Parametrization and Stokes' Theorem

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

Divergence of Vector Fields

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

Surface Integrals, Divergence Theorem

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

Differential Forms Integration

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

Surface Integrals: Parameterization and Divergence Theorem

Explores surface integrals using parameterization and the divergence theorem, with practical examples included.

Mathematics: Cylinders and Parametrizations

Discusses the mathematical concepts of cylinders and their parametrizations, including surface area, volume, and related exercises.

Curves with Poritsky Property and Liouville Nets

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

Applications of Residue Theorem in Complex Analysis

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Surface Integrals: Change of Variables

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