Lectures related to Advanced Analysis II: General Variable Change

Covers continuity, differentiation, and algebraic operations, including the computation of derivatives for various functions.

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Covers the inverse function theorem, Jacobian matrix, injective functions, bijective functions, and spherical coordinates.

Covers coordinate changes, focusing on polar and spherical coordinates and their transformations, determinants, and invertibility.

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.