Lectures related to 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.

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Provides solutions to an Analysis I exam, covering various topics.

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Presents the solution to finding the second-order Taylor polynomial of a function.

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Covers the concept of partial derivatives and their applications in mathematical analysis.

Covers calculating with Taylor series and convexity concepts, including sin(x) and cos(x) approximations.

Introduces Taylor series, covering their basics and applications in approximating functions and calculating limits.

Covers the concept of functions being n+1 times differentiable and the Taylor formula.

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

Covers the concept of functional derivatives and their calculation process with examples.

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

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

Introduces mathematical notations and functions essential for general physics.