Advanced Analysis II: Multi-Index and Taylor Formula

Related lectures (28)

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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.