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General |
MATH 464 , Spring 2010: Notes and Summary
| Lecture | Date | What was covered | Notes |
| 1 | Jan. 26 | Introduction | - |
| 2 | Jan. 28 | Review of analysis | get assignment 1 |
| 3 | Feb. 2 | Heat equation | return assignment 1 |
| 4 | Feb. 4 | ONB of Fourier series | get assignment 2 |
| 5 | Feb. 9 | ||
| 6 | Feb. 11 | ||
| 7 | Feb. 16 | Mean-square convergence. Examples | return assignment 2 |
| 8 | Feb. 18 | Parseval and Plancherel Formulae. L2 Optimality. | get assignment 3 |
| 9 | Feb. 23 | Pointwise convergence: Gibbs phenomenon. | |
| 10 | Feb. 25 | Fourier transform: inversion, Plancherel, Poisson summation formula | return assignment 3; get assignment 4 |
| 11 | Mar. 2 | Examples | |
| 12 | Mar. 4 | Properties of Fourier transform (1) | return assignment 4; get assignment 5 |
| 13 | Mar. 9 | Properties of Fourier Transform (2): Convolution | (MATH 0401) |
| 14 | Mar. 11 | Convolution of Fourier series | return assignment 5; get assignment 6(MATH0401) |
| 15 | Mar. 16 | No Class | Spring Break |
| 16 | Mar. 18 | No Class | Spring Break |
| - | Mar. 22 | REVIEW SESSION | 1-2pm and 5-6pm in CSIC 4122 |
| 17 | Mar. 23 | LTI and Fourier theory on Lp spaces | return assignment 6 |
| 18 | Mar. 25 | Mid Term Exam | MID TERM EXAM |
| 19 | Mar. 30 | Sampling of bandlimited functions: Shannon's formula | get assignment 7 |
| 20 | Apr. 1 | Oversampling and reconstruction with faster decay | |
| 21 | Apr. 6 | Short-Time Fourier Transform: Continuous-time case (Windowed Fourier Transform) | Quiz on Chapter 8 (MATH 0401) |
| 22 | Apr. 8 | Short-Time Fourier Transform: Discrete Time Case | return assignment 7; get assignment 8 (MATH 0401) |
| 23 | Apr. 13 | Examples of STFT analysis. Continuous Time Wavelet Transform | |
| 24 | Apr. 15 | Wavelets: Haar basis (I) | return assignment 8; get assignment 9 |
| 25 | Apr. 20 | Wavelets: Haar basis (II) | |
| 26 | Apr. 22 | 2-Scale Analysis Filterbank; Downsampler | return assignment 9; get assignment 10 |
| 27 | Apr. 27 | 2-Scale Analysis Filterbank; Upsampler | |
| 28 | Apr. 29 | Daubechies class D2N of FIR filterbanks | return assignment 10; get assignment 11 |
| 29 | May. 4 | MRA Wavelets | |
| 30 | May. 6 | PDEs (Heat equation; Wave equation) | return assignment 11 (MATH 0401) |
| 31 | May. 11 | PDEs (II) and Overview | Last Class |
