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General |
MATH 464 , Spring 2024: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section |
| 1 | Jan.25 | Introduction | Lecture 1 | 1.1 |
| 2 | Jan.30 | Review of linear algebra: Linear independence, spanning sets, bases, norms | get assignment 1, Lecture 2 | 1.1 |
| 3 | Feb. 1 | Review of linear algebra: scalar product, orthonormal bases, l^p spaces | Lecture 3, last pages | - |
| 4 | Feb. 6 | Fourier series (I) | return assignment 1; get assignment 2. Lecture 4, Matlab Code | 1.3 |
| 5 | Feb. 8 | Fourier series (II): L^2 theory | Lecture 5 | 1.3 |
| 6 | Feb.13 | Fourier series (III): pointwise convergence | return assignment 2; get assignment 3; Lecture 6 | 1.5 |
| 7 | Feb.15 | Fourier series: Gibbs phenomenon. | Matlab Code; Lecture 7 | 1.5 |
| 8 | Feb.20 | Approximation Errors and Summation Methods | Cesaro Summation vs. Symmetric Sum: Matlab code. | 1.5 |
| 9 | Feb.22 | Fourier transform: Examples, Rules for computing FT (I) | get assignment 4; return assignment 3; Lecture 8, Lecture 9 | 3.1, 3.2 |
| 10 | Feb.27 | Rules for computing FT (II); smoothnes vs. decay; Poisson summation formula | Lecture 10 | 3.3(153),4.2(193),1.4 (33-37) |
| 11 | Feb.29 | sine-cosine transforms; convolutions; integral equations | return assignment 4; get assignment 5; Lecture 11 | Problem 1.3; 2.1,2.2, 2.3 |
| 12 | Mar. 5 | convolutions - discrete signals & echo location | 1.2 (16-19), 2.3 (105-106) , 2.4 | |
| 13 | Mar. 7 | Sampling of bandlimited signals; Sannon formula; reconstruction error (I) | return assignment 5; get assignment 6;Lecture 13 | 8.1, 8.2, 8.4 |
| 14 | Mar.12 | Oversampling and reconstruction error (II) | Lecture 14 | 8.2, 8.4 |
| 15 | Mar.14 | Generalized function: Schwartz class of test functions. | return assignment 6; get assignment 7; Lecture 15 | 7.1 |
| - | Mar.17-24 | - | SPRING BREAK | - |
| 16 | Mar.26 | Continuous and Slowly Growing (CSG) Functions. Derivatives. | Lecture 16 | 7.1 |
| 17 | Mar.28 | Common Generalized Functions | return assignment 7; get assignment 8; Lecture 17 | 7.1 |
| - | Mar.27 | REVIEW SESSION | Kirwan Hall (MATH) 1313 | 5:00pm-7:00pm |
| 18 | Apr. 2 | MID-TERM EXAM | ||
| 19 | Apr. 4 | Distributions 1/x , 1/x2 | Lecture 18 | 7.2 |
| 20 | Apr. 9 | Translation, Dilation, Convolution, Products | Lecture 19 | 7.3 |
| 21 | Apr.11 | Derivative, Fourier transform | Lecture 20 | 7.3, 7.4 |
| 22 | Apr.16 | Algebraic and Differential Equations | return assignment 8, get assignment 9; Lecture 21 | 7.4 |
| 23 | Apr.18 | Differential Equations(II) | Lecture 22 | 7.4 |
| 24 | Apr.23 | PDE (I): Heat/Wave Equation | 9.2 | |
| 25 | Apr.25 | PDE (II): Wave Equation | return assignment 9, get assignment 10; 2024 Lecture 24 file, old Lecture 24 | 9.2, 9.3 |
| 26 | Apr.30 | Windowed Fourier Transform (1) | Lecture 25 | 9.3 |
| 27 | May 2 | Windowed Fourier Transform (II) | return assignment 10, get assignment 11 Matlab code Pdf file; Lecture 26 |
11.2, 11.3, 11.4 |
| 28 | May 7 | Continuous Wavelet Transform | Lecture 27 | 11.2, 11.3, 11.4 |
| 29 | May 9 | Uncertainty Inequalities; Applied Harmonic Analysis | return assignment 11; Last Class | 11.4, 12.4 (pg. 761) |
| - | May 9 | REVIEW SESSION | Kirwan Hall (MATH) 1308 | 5:00pm-7:00pm |
| - | May 13 | FINAL EXAM | MTH 0305 | 8:00am-10:00am |
