Lectures related to Functional Determinants and Gelfand-Yaglom Theorem

Explores Riemann integrability, the fundamental theorem of integral calculus, and various integration techniques.

Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.

Covers local invertibility of vector fields and the Inverse Function Theorem.

Explains the Fundamental Theorem of Calculus, focusing on integrals and their relationship with primitives.

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Covers Taylor approximation, convex functions, and integrable properties.

Explores examples of applying the change of variables formula to simplify integrals over different regions in the xy-plane.

Covers Cramer's Rule, matrix inverse, determinants, and volume in linear algebra.

Covers integration by change of variables and the derivation in chain rule.