Lecture

Directional Derivatives

Related lectures (22)

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Covers the concept and calculation of directional derivatives in multivariable calculus.

Explores conditions for non-differentiability in multivariable calculus and the implications of the differentiability theorem.

Chain Rules

Explores the extension of the chain rule to higher dimensions and compositions of functions.

Directional Derivatives and Tangent Planes

Explores directional derivatives, tangent planes, and function differentiability in multivariable calculus.

Limits of Functions in R^n

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

Differentiability of Functions of Several Variables

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

Calculus of Variations: Some Topics

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Derivative Chain Rule

Covers the derivative of the composition of two functions and the chain rule theorem.

Functions with Multiple Variables

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Directional Derivatives

Explores directional derivatives, their calculation, examples, and cases of lack of continuity.

Partial Derivatives and Functions

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

Differentiability and Composition

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Directional Derivative: Definitions and Examples

Covers the definition of directional derivatives and their applications in two dimensions.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Gradient: Scalar Field

Explores gradient in scalar fields, directional derivatives, and level sets.

Functions with Values in R^m

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