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.