Functions: Multivariable Functions and Exact Differentials

This lecture delves into the concept of expressing functions as a function of time and space, exploring the implications of moving reference frames and fluid dynamics. The instructor explains the differentiation of multivariable functions and the conditions for exact differentials, providing examples to illustrate the concepts. The lecture also touches on the significance of exact differentials in thermodynamics and the implications for integration paths. Additionally, the discussion extends to the gradient of a multivariable function, introducing the concepts of curls and gradients in the context of vector partial derivatives.