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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