Analysis I: Limits and Continuity

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

Explains how to find local extrema of functions using derivatives and critical points.

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

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Explores functions of class C^p, emphasizing continuity and differentiability properties.