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Content of the lectures:
Chapter 1
Date
|
Content
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30/jan/13
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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
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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
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The Gamma Γ function and
the ζ function (§1.2.3).
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20/feb/13
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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
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Discrete wavelets (D4) (§1.3.3). |
Chapter 2
Date
|
Content
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06/mar/13
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Uncertainty principle, Hardy's theorem (§2.1.1). |
11/mar/13
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Heisenberg's inequality, Gibbs phenomenon (§2.1.1). |
13/mar/13
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Quantum mechanics, Schrödinger equation (§2.1.2). |
Special lectures (Prof. J. Jimenez-Urroz)
Date
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Content
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19/mar/13
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DFT and quadratic reciprocity.
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20/mar/13
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DFT and quadratic reciprocity. |
21/mar/13
|
L-functions (Dirichlet and elliptic curves). |
Chapter 2
Date
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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
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First steps in diffraction models (§2.2.2). |
22/apr/13
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Kirchhoff formula, Fraunhofer diffraction (§2.2.2). |
27/apr/13
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Basic van der Corput estimates (§2.3.1). |
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