Advanced Analysis I: Taylor Formula and Limit Development

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.

Explores approximating functions with Taylor series, showcasing step-by-step calculations and practical applications.

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.