Lecture
This lecture covers the concept of partial derivatives and functions in the context of multivariable calculus. It explains the definition and properties of partial derivatives, focusing on their existence and continuity. The instructor demonstrates how to calculate partial derivatives and emphasizes the importance of well-defined functions. The lecture also discusses the geometric interpretation of partial derivatives and their role in determining the direction of steepest ascent. Examples are provided to illustrate the application of partial derivatives in various scenarios, highlighting their significance in mathematical analysis.