Functions: Differentials, Taylor Expansions, Integrals

This lecture covers the fundamental concepts of functions, including limits, continuity, and differentiability. It explores the use of sequences to define these notions and focuses on differentiability, tangents, and common derivatives. The lecture also delves into the L'Hôpital rule, Taylor expansions, and integrals, providing examples and applications in physical models. Additionally, it discusses the Taylor series, its convergence, and the importance of a-dimensional arguments in functions. The lecture concludes with the concept of primitives and integrals, preparing students for advanced techniques like change of variables and multi-variable functions.