Lectures related to Mathematical fallacy

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

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

Differential Forms Integration

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

Curves with Poritsky Property and Liouville Nets

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

Fixed Point Theorem: Convergence of Newton's Method

Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.

Applications of Residue Theorem in Complex Analysis

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