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General |
MATH 464 , Spring 2011: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section |
| 1 | Jan. 25 | Introduction | - | 1.1 |
| 2 | Jan. 27 | Class canceled | - | |
| 3 | Feb. 1 | Review of analysis | get assignment 1 | - |
| 4 | Feb. 3 | Fourier series (I) | return assignment 1; get assignment 2. Matlab Code | 1.3 |
| 5 | Feb. 8 | Fourier series (II): L^2 theory | return assignment 2 | 1.3 |
| 6 | Feb. 10 | Fourier series (III): pointwise convergence | get assignment 3 | 1.5 |
| 7 | Feb. 15 | Fourier series: Gibbs phenomenon. Fourier transform | return assignment 3; get assignment 4. Matlab Code | 1.5 |
| 8 | Feb. 17 | Fourier transform: Examples | 3.1 | |
| 9 | Feb. 22 | Rules for computing FT (I) | return assignment 4; get assignment 5 | 3.2 |
| 10 | Feb. 24 | Rules for computing FT (II); smoothnes vs. decay; Poisson summation formula | 3.3(153),4.2(193),1.4 (33-37) | |
| 11 | Mar. 1 | sine-cosine transforms; convolutions; integral equations | Problem 1.3; 2.1,2.2, 2.3 | |
| 12 | Mar. 3 | convolutions - discrete signals & echo location | return assignment 5; get assignment 6 |
1.2 (16-19), 2.3 (105-106) , 2.4 |
| 13 | Mar. 8 | Sampling of bandlimited signals; Sannon formula; reconstruction error (I) | 8.1, 8.2, 8.4 | |
| 14 | Mar. 10 | Oversampling and reconstruction error (II) | return assignment 6; get assignment 7 | 8.2, 8.4 |
| 15 | Mar. 15 | Generalized function: Schwartz class of test functions | 7.1 | |
| 16 | Mar. 17 | Continuous and Slowly Growing (CSG) Functions. Derivative | return assignment 7 | 7.1 |
| - | Mar. 17 | REVIEW SESSION | CSIC 4122 | 10:30am-12:15noon, 3:30pm-5:00pm |
| 17 | Mar. 22 | No Class | Spring Break | |
| 18 | Mar. 24 | No Class | Spring Break | |
| 19 | Mar. 29 | Mid Term Exam | MID TERM EXAM | |
| 20 | Mar. 31 | Common Generalized Functions | get assignment 8 | 7.2 |
| 21 | Apr. 5 | 1/x , 1/x2 | 7.2 | |
| 22 | Apr. 7 | Translation, Dilation, Convolution, Products | 7.3 | |
| 23 | Apr. 12 | Derivative, Fourier transform | 7.3, 7.4 | |
| 24 | Apr. 14 | Equations | return assignment 8, get assignment 9 | 7.4 |
| 25 | Apr. 19 | Differential Equations(II) | 7.4 | |
| 26 | Apr. 21 | Wave Equation | return assignment 9, get assignment 10 |
9.2 |
| 27 | Apr. 26 | Wave/Heat Equation | 9.2, 9.3 | |
| 28 | Apr. 28 | Heat Equation (II) | return assignment 10, get assignment 11 |
9.3 |
| 29 | May. 3 | Short-Time Fourier Transform (I) | Matlab code Pdf file |
11.2, 11.3, 11.4 |
| 30 | May. 5 | Short-Time Fourier Transform (II) | return assignment 11 | 11.2, 11.3, 11.4 |
| 31 | May. 10 | Uncertainty Inequalities; Applied Harmonic Analysis | Last Class | 11.4, 12.4 (pg. 761) |
