Lectures related to Functions with Values in R^m

Explores linear differential of functions, continuity, differentiability, and matrix representation.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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

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

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

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

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

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.