Lectures related to Pure mathematics

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Discusses the residue theorem and its applications in calculating complex integrals.

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.