Lectures related to Partial Derivatives: Definitions and Applications

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Introduces partial derivatives in functions of several variables and their properties.

Explains the concept of partial derivatives through various examples involving functions of two variables.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.