Lectures related to Differentiable Functions in R²

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

Explores Rolle's Theorem for continuous and differentiable functions on closed intervals.

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

Explores Taylor series expansions for derivatives and integrals, including practical applications.

Covers Fermat's theorem, necessary optimality conditions, convexity, and eigenvalue curvature in optimization.

Covers Rolle's Theorem and the Mean Value Theorem with illustrative examples.