Lectures related to Advanced Analysis II: Multi-Index and Taylor Formula

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

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Introduces the kernel of a linear application and its properties.

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

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

Covers the method to calculate the images of vectors in a given base.

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Explains partial derivatives, Hessienne matrix, and their properties.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

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

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

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

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.