Chapter 1

Date	Content
30/jan/13	Definition of Fourier series and integrals, basic convergence results (§1.1.1, §1.1.2).
4/feb/13	The L2 theory, numerical examples (§1.1.2, §1.1.3).
6/feb/13	Partial summation (§1.2.1).
11/feb/13	Poisson summation, Euler-Maclaurin (§1.2.2).
13/feb/13	Finite order entire functions, analytic extension (§1.2.3).
18/feb/13	The Gamma Γ function and the ζ function (§1.2.3).
20/feb/13	Discrete transfroms and characters (§1.3.1).
25/feb/13	DCT and JPEG (§1.3.2 and §1.3.3).
27/feb/13	More on JPEG, filters (§1.3.3).
04/mar/13	Discrete wavelets (D4) (§1.3.3).

Chapter 2

Date	Content
06/mar/13	Uncertainty principle, Hardy's theorem (§2.1.1).
11/mar/13	Heisenberg's inequality, Gibbs phenomenon (§2.1.1).
13/mar/13	Quantum mechanics, Schrödinger equation (§2.1.2).

Special lectures (Prof. J. Jimenez-Urroz)

Date	Content
19/mar/13	DFT and quadratic reciprocity.
20/mar/13	DFT and quadratic reciprocity.
21/mar/13	L-functions (Dirichlet and elliptic curves).

Chapter 2

Date	Content
03/apr/13	Quantum free particle (§2.1.2).
08/apr/13	Operators, quantum mechanics and uncertainty (§2.1.2).
10/apr/13	The principle of stationary phase (§2.2.1).
15/apr/13	Van der Corput Lemmas, Bessel function J_1 (§2.2.1).
17/apr/13	First steps in diffraction models (§2.2.2).
22/apr/13	Kirchhoff formula, Fraunhofer diffraction (§2.2.2).
27/apr/13	Basic van der Corput estimates (§2.3.1).