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General |
MATH 464 , Fall 2020: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section |
| 1 | Sep. 1 | Introduction | L1 | 1.1 |
| 2 | Sep. 3 | Review of linear algebra: Linear independence, spanning sets, bases, norms | L2 , get assignment 1 | 1.1 |
| 3 | Sep. 8 | Review of linear algebra: scalar product, orthonormal bases, l^p spaces | L3, L3extra (optional) | - |
| 4 | Sep.10 | Fourier series (I) | return assignment 1; get assignment 2. Matlab Code, L4 | 1.3 |
| 5 | Sep.15 | Fourier series (II): L^2 theory | L5 | 1.3 |
| 6 | Sep.17 | Fourier series (III): pointwise convergence | return assignment 2; get assignment 3, L6 | 1.5 |
| 7 | Sep.22 | Fourier series: Gibbs phenomenon. | Matlab Code, L7 | 1.5 |
| 8 | Sep.24 | Fourier transform: Examples | return assignment 3; get assignment 4, L8 | 3.1 |
| 9 | Sep.29 | Rules for computing FT (I) | L9 | 3.2 |
| 10 | Oct. 1 | Rules for computing FT (II); smoothnes vs. decay; Poisson summation formula | L10, return assignment 4; get assignment 5 | 3.3(153),4.2(193),1.4 (33-37) |
| 11 | Oct. 6 | sine-cosine transforms; convolutions; integral equations | L11 | Problem 1.3; 2.1,2.2, 2.3 |
| 12 | Oct. 8 | convolutions - discrete signals & echo location | return assignment 5; get assignment 6; L12 |
1.2 (16-19), 2.3 (105-106) , 2.4 |
| 13 | Oct. 13 | Sampling of bandlimited signals; Sannon formula; reconstruction error (I) | L13 | 8.1, 8.2, 8.4 |
| 14 | Oct.15 | Oversampling and reconstruction error (II) | L14, return assignment 6 | 8.2, 8.4 |
| - | Oct.16 | REVIEW SESSION | Class Zoom Link | 11:00am-1:00pm |
| 15 | Oct.20 | Mid Term Exam | MID TERM EXAM | 3:30pm-4:45pm |
| 16 | Oct.22 | Generalized function: Schwartz class of test functions | L15, get assignment 7 | 7.1 |
| 17 | Oct.27 | Continuous and Slowly Growing (CSG) Functions. Derivative | L16 | 7.1 |
| 18 | Oct.29 | Common Generalized Functions | L17 | 7.2 |
| 19 | Nov. 3 | 1/x , 1/x2 | L18, return assignment 7; get assignment 8 | 7.2 |
| 20 | Nov. 5 | Translation, Dilation, Convolution, Products | L19 | 7.3 |
| 21 | Nov.10 | Derivative, Fourier transform | L20 | 7.3, 7.4 |
| 22 | Nov.12 | Algebraic and Differential Equations | L21, return assignment 8, get assignment 9 | 7.4 |
| 23 | Nov.17 | Differential Equations(II) | L22 | 7.4 |
| 24 | Nov.19 | Heat Equation | L23, return assignment 9, get assignment 10 | 9.3 |
| 25 | Nov.24 | Wave Equation. Vibrating String | L24 | 9.2, 9.3 |
| 26 | Nov.26 | - | THANKSGIVING | No Class |
| 27 | Dec. 1 | Short-Time Fourier Transform/Windowed Fourier Transform (I) | L25, Matlab code Pdf file |
11.2, 11.3, 11.4 |
| 28 | Dec. 3 | Short-Time Fourier Transform/Windowed Fourier Transform (II) | L26, return assignment 10, get assignment 11 | 11.2, 11.3, 11.4 |
| 28 | Dec. 8 | Continuous Wavelet Transform. Time-Frequency Localization | L27 | 10, 11.4, 12.4 |
| - | Dec. 9 | REVIEW SESSION | Class Zoom Link | 3:00pm - 5:00pm |
| 29 | Dec. 10 | Mid-Term Exam (II) | return assignment 11; Last Class | 11.4, 12.4 (pg. 761) |
| - | Dec. 18 | REVIEW SESSION | Class Zoom Link | 2:00pm-4:00pm |
| - | Dec. 22 | FINAL EXAM | Class Zoom Link | 10:30am-12:30pm |
