Sumários
Lecture 14: Fourier Transform, part III. Sobolev Spaces, part I
13 Abril 2018, 11:00 • Hugo Tavares
The derivative of a temperate distribution is a temperate distribution. A
polynomial times a tempered distribution is a tempered distribution. Formulas for derivatives of tempered distributions.
Introduction to the Sobolev Spaces W^{k,p}(Omega): definition, norms, examples, elementary properties.
Lecture 13. Fourier Transform, part II
10 Abril 2018, 14:00 • Hugo Tavares
The Fourier Transform and its inverse from the Schwartz space into itself,
Extension to L^2: Plancherel's and Parseval's formulas. Examples.
Lecture 12: Distributions part II; Fourier Transform part I
6 Abril 2018, 11:00 • Hugo Tavares
Higher order derivative of a distribution. COmputation of the derivative of the fundamental solution of the Laplace Equation in the sense of distributions.
Definition of Fourier Transform and Inverse Fourier Transform in L^1.
The Schwartz space, definition of convergence and some continuous embeddings.
Exercise class 6
5 Abril 2018, 11:00 • Hugo Tavares
The heat and wave equations: solution of exercises 1, 2 and 4 of Exercise Sheet 4.
Distributions: solution to exercise 3a) of Exercise Sheet 5.