Lectures related to Advanced Analysis II: Hessians and Directional Derivatives

Explores finding the equation of the tangent line to a function's graph at a point.

Explains partial derivatives, Hessienne matrix, and their properties.

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Explores differentiable functions, Taylor approximations, and directional derivatives in open sets.

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

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

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

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

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Explores derivability, continuity, and composite functions with illustrative examples.

Explores partial derivatives, gradient, directional derivatives, and differentiability in determining slopes.

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

Explores derivatives, Hessians, and Taylor approximations for differentiable functions.

Covers directional derivative, differentiability, and gradient matrices, emphasizing the first order.

Explores directional derivatives, showcasing scenarios where they exist but the function is not differentiable.

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

Explores differentiability theorems, including partial derivatives, existence of derivatives, and Schwartz's theorem reciprocals.

Introduces partial derivatives, directional derivatives, and differentiability of functions with examples and the Schwartz theorem.

Covers differentiable functions, derivatives, and tangent planes in mathematics.