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General |
MATH 464 , Fall 2013: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section |
| 1 | Sept. 3 | Introduction; Continuity and Differentiability | get assignment 1 | - |
| 2 | Sept. 5 | Integrability (L1, L2, Lp spaces); Vector Spaces | - | - |
| 3 | Sept. 10 | Orthonormal Bases; Linear Independence, Spanning; Orthogonal Projections | - | - |
| 4 | Sept. 12 | Fourier series (I): Definition and examples | turn in assignment 1; get assignment 2. Matlab Code | 1.3 |
| 5 | Sept. 17 | Fourier series (II): L^2 theory | turn in assignment 2 | 1.3 |
| 6 | Sept. 19 | Fourier series (III): pointwise convergence | get assignment 3 | 1.5 |
| 7 | Sept. 24 | Fourier series: Gibbs phenomenon; mean-square and pointwise approximation error estimates | turn in assignment 3; get assignment 4. Matlab Code | 1.5 |
| 8 | Sept. 26. | Fourier Series: Heat Equation; Other Examples | - | 1.1, 3.1 |
| - | Sept. 30 | REVIEW SESSION in Kim Jeong Building: KEB 1200 |
turn in assignment 4 before Review Session; 5-7pm KEB 1200 |
- |
| 9 | Oct. 1 | MID-TERM 1 | CSIC 4122 | Chapters 1, (selected topics of) 4, Chapter 9, sect.9.3 (pages 548-553) |
| 10 | Oct. 3 | Fourier transform: Definition; Examples | 3.1 | |
| 11 | Oct. 8 | Plancherel Formula; Poisson Summation Formula | get assignment 5 | 3.2, 1.4 (33-37) |
| 12 | Oct. 10 | Rules for computing FT (I) | 3.2 | |
| 13 | Oct. 15 | Rules for computing FT (II); smoothnes vs. decay; sine-cosine transforms | turn in assignment 5; get assignment 6; EGR 1110 | 3.3(153),4.2(193), |
| 14 | Oct.17 | convolutions; integral equations | EGR 1110; |
Problem 1.3; 2.1,2.2, 2.3 |
| 15 | Oct. 22 | Sampling of bandlimited signals; Shannon formula; reconstruction error (I) | turn in assignment 6; get assignment 7 | 8.1, 8.2, 8.4 |
| 16 | Oct. 24 | Oversampling and reconstruction error (II) | 8.2, 8.4 | |
| 17 | Oct. 29 | convolutions - discrete signals & Fourier series | turn in assignment 7;get assignment 8 | 1.2 (16-19), 2.3 (105-106) , 2.4 |
| - | Oct. 29 | REVIEW SESSION | MATH 0304 | 3:00pm - 5:00pm |
| 18 | Oct. 31 | MID-TERM 2 | CSIC 4122 | |
| 19 | Nov. 5 | Windowed Fourier transform - analysis/synthesis and L2 | turn in assignment 8; get assignment 9 | 11.2, 11.3, 11.4 |
| 20 | Nov. 7 | wFT - Time and Frequency separation / Instantaneous Frequency (1) | spectrogram code | 11.2, 11.3, 11.4 |
| 21 | Nov. 12 | Short-Time Fourier Transform - discrete time | turn inassignment 9; get assignment 10 | 11.2, 11.3, 11.4 |
| 22 | Nov. 14 | Instantaneous Frequency (2); Time- and Band-limited functions | 11.4 , 12.4 (pg. 761) | |
| 23 | Nov. 19 | Uncertainty Inequality; Continuous Wavelet Transform | turn in assignment 10; get assignment 11 | 11.4 , 12.4 (pg. 761) |
| 24 | Nov. 21 | cWT - Analysis and Synthesis; Examples | 10.1 | |
| 25 | Nov. 26 | Wavelet Bases: Haar Basis (1) | 10.1 | |
| 26 | Nov. 28 | THANKSGIVING BREAK | No Class | |
| 27 | Dec.3 | Haar Basis (2) | turn in assignment 11; get assignment 12 | 10.1 |
| 28 | Dec.5 | Haar Basis & MRA | 10.2 | |
| 29 | Dec.10 | MRA | 10.2, 10.3 | |
| 30 | Dec.12 | MRA | turn in assignment 12; Last Class |
10.3 |
| - | Dec.12 | REVIEW SESSION | MATH 0401 | 2:00pm - 4:30pm |
| - | Dec.16 | FINAL EXAM | CSIC 4122 | Comprehensive |
