Advanced Analysis II: Tangent Plan and Differentiability

This lecture covers the concept of tangent planes and differentiability in advanced analysis, focusing on the definition and properties of tangent planes, as well as the differentiability of functions in multiple variables. The instructor reviews the notion of tangent planes, the graph of a function, and the existence of tangent planes at specific points. The lecture also delves into the differentiability of functions, discussing the conditions for a function to be differentiable at a point. Various examples and mathematical notations are used to illustrate these concepts.