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MATH 464 , Spring 2011: Notes and Summary

 Lecture Date What was covered Notes Textbook Section 1 Jan. 25 Introduction - 1.1 2 Jan. 27 Review of analysis Class canceled - 3 Feb. 1 Review of analysis get assignment 1 - 4 Feb. 3 Fourier series (I) return assignment 1; get assignment 2. Matlab Code 1.3 5 Feb. 8 Fourier series (II): L^2 theory return assignment 2 1.3 6 Feb. 10 Fourier series (III): pointwise convergence get assignment 3 1.5 7 Feb. 15 Fourier series: Gibbs phenomenon. Fourier transform return assignment 3; get assignment 4. Matlab Code 1.5 8 Feb. 17 Fourier transform: Examples 3.1 9 Feb. 22 Rules for computing FT (I) return assignment 4; get assignment 5 3.2 10 Feb. 24 Rules for computing FT (II); smoothnes vs. decay; Poisson summation formula 3.3(153),4.2(193),1.4 (33-37) 11 Mar. 1 sine-cosine transforms; convolutions; integral equations Problem 1.3; 2.1,2.2, 2.3 12 Mar. 3 convolutions - discrete signals & echo location return assignment 5; get assignment 6 1.2 (16-19), 2.3 (105-106) , 2.4 13 Mar. 8 Sampling of bandlimited signals; Sannon formula; reconstruction error (I) 8.1, 8.2, 8.4 14 Mar. 10 Oversampling and reconstruction error (II) return assignment 6; get assignment 7 8.2, 8.4 15 Mar. 15 Generalized function: Schwartz class of test functions 7.1 16 Mar. 17 Continuous and Slowly Growing (CSG) Functions. Derivative return assignment 7 7.1 - Mar. 17 REVIEW SESSION CSIC 4122 10:30am-12:15noon, 3:30pm-5:00pm 17 Mar. 22 No Class Spring Break 18 Mar. 24 No Class Spring Break 19 Mar. 29 Mid Term Exam MID TERM EXAM 20 Mar. 31 Common Generalized Functions get assignment 8 7.2 21 Apr. 5 1/x , 1/x2 7.2 22 Apr. 7 Translation, Dilation, Convolution, Products 7.3 23 Apr. 12 Derivative, Fourier transform 7.3, 7.4 24 Apr. 14 Equations return assignment 8, get assignment 9 7.4 25 Apr. 19 Differential Equations(II) 7.4 26 Apr. 21 Wave Equation return assignment 9, get assignment 10 9.2 27 Apr. 26 Wave/Heat Equation 9.2, 9.3 28 Apr. 28 Heat Equation (II) return assignment 10, get assignment 11 PDE solutions 9.3 29 May. 3 Short-Time Fourier Transform (I) Matlab code Pdf file 11.2, 11.3, 11.4 30 May. 5 Short-Time Fourier Transform (II) return assignment 11 11.2, 11.3, 11.4 31 May. 10 Uncertainty Inequalities; Applied Harmonic Analysis Last Class 11.4, 12.4 (pg. 761)