Advanced Analysis II: Differentiable Functions

This lecture covers the concept of differentiable functions, focusing on the case of a differentiable function in an open set. It explains the properties of differentiable functions in a given domain and their derivatives. The lecture also delves into the application of Taylor approximations and the development of limits. Additionally, it discusses the directional derivative and partial derivatives, emphasizing the importance of understanding the symmetrical nature of Hessians. The content includes examples and applications of differentiable functions in various contexts.