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General |
MATH 464 , Fall 2012: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section |
| 1 | Aug. 30 | Inroduction/Review of Analysis/Review of Linear Spaces with Scalar Product | get assignment 1 | 1.1 |
| 2 | Sept. 4 | Review (cont.); Fourier Series - heat equation | - | 9.3 (548-553) |
| 3 | Sept. 6 | Fourier series (I) | turn in assignment 1 | 1.3 |
| 4 | Sept. 11 | Fourier series (II) | turn in assignment 2 | 1.3 |
| 5 | Sept. 13 | Fourier series (III): L^2 theory; Plancherel theorem; mean square approximation error |
- | 1.3, 1.5 |
| 6 | Sept. 18 | Fourier series (IV): pointwise convergence, Dirichlet criterion; Gibbs Phenomenon; Numerical Approximations | Matlab code: convergence, Gibbs; turn in assignment 3 | 1.5 |
| 7 | Sept. 20 | Fourier transform: Definition, L2 theory | - | 1.5 |
| 8 | Sept. 25 | Rules for computing FT;sine-cosine transforms; convolutions; integral equations | turn in assignment 4 | 3.1, 3.2; Problem 1.3 |
| 9 | Sept. 27 | Differential equations; Poisson Sum formula | - | 3.2 |
| 10 | Oct. 2 | Convolutions (1) | turn in assignment 5 | 2.1,2.2, 2.3 |
| 11 | Oct. 4 | Convolutions (2) | turn in assignment 6 | 1.2,2.3,2.4,3.3(153),4.2(193) |
| - | Oct. 5 | REVIEW SESSION | 3:00-5:00pm | CSIC 4122 |
| 12 | Oct. 9 | TEST 1 | - | - |
| 13 | Oct. 11 | Sampling of bandlimited signals; Sannon formula; reconstruction error (I) | - | 8.1, 8.2, 8.4 |
| 14 | Oct. 16 | Oversampling and reconstruction error (II) | - | 8.2, 8.4 |
| 15 | Oct. 18 | Reconstruction error (III); Generalized Function: Schwartz class of test functions | - | 8.4, 7.1 |
| 16 | Oct. 23 | Continuous and Slowly Growing (CSG) functions. | turn in assignment 7 | 7.1 |
| 17 | Oct. 25 | Derivative of a distribution. Common generalized functions | Class in CSI 1122 | 7.2 |
| 18 | Oct. 30 | CANCELED DUE TO HURRICANE SANDY | see file | |
| 19 | Nov. 1 | Distributions: 1/x and Fourier transform | turn in assignment 8 | 7.3 |
| 20 | Nov. 6 | Distributions: Convolutions, Algebraic and Ordinary Differential Equations | Class in CSI 1122 | 7.3, 7.4 |
| 21 | Nov. 8 | Applications of Fourier transform to distributions; Periodic distributions | Class in CSI 1122; turn in assignment 9 | 7.5, 7.7 |
| - | Nov. 9, noon | TURN IN ASSIGNMENT 9 | CSI 4131 | - |
| - | Nov. 12 | REVIEW SESSION | 5:00pm-7:00pm | CSIC 4122 |
| 22 | Nov. 13 | TEST 2 | - | - |
| 23 | Nov. 15 | PDE: Wave Equation | - | 9.2 |
| 24 | Nov. 20 | PDE: Heat Equation (I) | - | 9.3 |
| 25 | Nov. 22 | No Class | - | Thanksgiving Break |
| 26 | Nov. 27 | PDE: Heat Equation (II) | - | 9.3 |
| 27 | Nov. 29 | Windowed Fourier Transform (I) | turn in assignment 10 | 11.2 , 11.3 , 11.4 |
| 28 | Dec. 4 | Windowed Fourier Transform (II)/Wavelet Transform (I) | Here is some Matlab code. | 11.4 |
| 29 | Dec. 6 | Wavelet Transform (II) | - | - |
| 30 | Dec. 11 | Uncertainty Inequality; Instantaneous Frequency | turn in assignment 11; Last Class | - |
