Lectures related to Partial Derivatives: Definitions and Applications

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Limits and Derivatives in Multivariable Functions

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Implicit Function Theorem: Tangent Planes and Derivatives

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Recurrence Method: Generalization and Differential Calculus

Explores the fundamental principle of the recurrence method and differential calculus of functions of several variables.

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Partial Derivatives: Higher Order and Applications

Covers the concept of partial derivatives of higher order and their applications in various contexts.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Limits of Functions in R^n

Explores limits of functions in R^n and the importance of understanding derivatives in multiple dimensions.

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Partial Derivatives: Introduction

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

Partial Derivatives: Examples

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.