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MATH 464 , Spring 2017: Notes and Summary

 Lecture Date What was covered Notes Textbook Section 1 Jan. 26 Introduction - 1.1 2 Jan. 31 Review of linear algebra: Linear independence, spanning sets, bases, norms get assignment 1 1.1 3 Feb. 2 Review of linear algebra: scalar product, orthonormal bases, l^p spaces - - 4 Feb. 7 Fourier series (I) return assignment 1; get assignment 2. Matlab Code 1.3 5 Feb. 9 Fourier series (II): L^2 theory 1.3 6 Feb.14 Fourier series (III): pointwise convergence return assignment 2; get assignment 3 1.5 7 Feb.16 Fourier series: Gibbs phenomenon. Matlab Code 1.5 8 Feb.21 Fourier transform: Examples return assignment 3; get assignment 4. 3.1 9 Feb.23 Rules for computing FT (I) 3.2 10 Feb.28 Rules for computing FT (II); smoothnes vs. decay; Poisson summation formula return assignment 4; get assignment 5 3.3(153),4.2(193),1.4 (33-37) 11 Mar. 2 sine-cosine transforms; convolutions; integral equations Problem 1.3; 2.1,2.2, 2.3 12 Mar. 7 convolutions - discrete signals & echo location return assignment 5; get assignment 6 1.2 (16-19), 2.3 (105-106) , 2.4 13 Mar. 9 Sampling of bandlimited signals; Sannon formula; reconstruction error (I) 8.1, 8.2, 8.4 14 Mar.14 Oversampling and reconstruction error (II) return assignment 6; get assignment 7 8.2, 8.4 - Mar.14 - REVIEW SESSION CSIC 4122, 3:30pm-5:30pm - Mar.15 - return assignment 6; REVIEW SESSION; get assignment 7 MATH 0402, 1:00pm-3:00pm 15 Mar.16 Mid Term Exam MID TERM EXAM - - Mar.20-24 - SPRING BREAK - 16 Mar.28 Oversampling and reconstruction error (II). Generalized function: Schwartz class of test functions 8.2, 8.4, 7.1 17 Mar.30 Continuous and Slowly Growing (CSG) Functions. Derivative - 7.1 18 Apr. 4 Common Generalized Functions return assignment 7; get assignment 8 7.2 19 Apr. 6 1/x , 1/x2 7.2 20 Apr.11 Translation, Dilation, Convolution, Products 7.3 21 Apr.13 Derivative, Fourier transform 7.3, 7.4 22 Apr.18 Algebraic and Differential Equations return assignment 8, get assignment 9 7.4 23 Apr.20 Differential Equations(II) 7.4 24 Apr.25 Wave Equation return assignment 9, get assignment 10 9.2 25 Apr.27 Wave/Heat Equation 9.2, 9.3 26 May 2 Heat Equation (II) 9.3 27 May 4 Short-Time Fourier Transform (I) return assignment 10, get assignment 11Matlab code Pdf file 11.2, 11.3, 11.4 28 May 9 Short-Time Fourier Transform (II) 11.2, 11.3, 11.4 29 May 11 Uncertainty Inequalities; Applied Harmonic Analysis return assignment 11; Last Class 11.4, 12.4 (pg. 761) - May 12 REVIEW SESSION CSIC 4122 2:00pm-4:00pm - May 17 FINAL EXAM CSIC 4122 10:30am-12:30pm