Partial Derivatives and Gradient

This lecture covers the definitions and properties of partial derivatives, emphasizing their dependence on the coordinates of a function. It also introduces the concept of the gradient, explaining its geometric interpretation and its role in defining functions. The lecture further explores the interpretation of gradients in two-dimensional space and discusses the directional derivatives. Additionally, it delves into the geometric interpretation of gradients, providing examples and illustrations to aid in understanding. The lecture concludes with a detailed explanation of how gradients can be used to define functions and their significance in various mathematical contexts.