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MATH 464 , Fall 2015: Notes and Summary

 Lecture Date What was covered Notes Textbook Section 1 Sep. 1 Introduction - 1.1 2 Sep. 3 Review of linear algebra: Linear independence, spanning sets, bases, norms get assignment 1 1.1 3 Sep. 8 Review of linear algebra: scalar product, orthonormal bases, l^p spaces - - 4 Sep.10 Fourier series (I) return assignment 1; get assignment 2. Matlab Code 1.3 5 Sep.15 Fourier series (II): L^2 theory return assignment 2 1.3 6 Sep.17 Fourier series (III): pointwise convergence get assignment 3 1.5 7 Sep.22 Fourier series: Gibbs phenomenon. Matlab Code 1.5 8 Sep.24 Fourier transform: Examples return assignment 3; get assignment 4. 3.1 9 Sep.29 Rules for computing FT (I) 3.2 10 Oct. 1 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 Oct. 6 sine-cosine transforms; convolutions; integral equations Problem 1.3; 2.1,2.2, 2.3 12 Oct. 8 convolutions - discrete signals & echo location return assignment 5; get assignment 6 1.2 (16-19), 2.3 (105-106) , 2.4 13 Oct. 13 Sampling of bandlimited signals; Sannon formula; reconstruction error (I) 8.1, 8.2, 8.4 14 Oct.15 Oversampling and reconstruction error (II) return assignment 6; get assignment 7 8.2, 8.4 - Oct.15 REVIEW SESSION MATH 0401 2:00pm-4:00pm 15 Oct.20 Mid Term Exam MID TERM EXAM - 16 Oct.22 Generalized function: Schwartz class of test functions 7.1 17 Oct.27 Continuous and Slowly Growing (CSG) Functions. Derivative return assignment 7 7.1 18 Oct.29 Common Generalized Functions get assignment 8 7.2 19 Nov. 3 1/x , 1/x2 7.2 20 Nov. 5 Translation, Dilation, Convolution, Products 7.3 21 Nov. 10 Derivative, Fourier transform 7.3, 7.4 22 Nov.12 Algebraic and Differential Equations return assignment 8, get assignment 9 7.4 23 Nov.17 Differential Equations(II) 7.4 24 Nov.19 Wave Equation return assignment 9, get assignment 10 9.2 25 Nov.24 Wave/Heat Equation 9.2, 9.3 - Nov.26 - THANKSGIVING No Class 26 Dec. 1 Heat Equation (II) 9.3 27 Dec. 3 Short-Time Fourier Transform (I) return assignment 10, get assignment 11Matlab code Pdf file 11.2, 11.3, 11.4 28 Dec. 8 Short-Time Fourier Transform (II) 11.2, 11.3, 11.4 29 Dec.10 Uncertainty Inequalities; Applied Harmonic Analysis return assignment 11; Last Class 11.4, 12.4 (pg. 761) - Dec.10 REVIEW SESSION MATH 0305 4:00pm-6:00pm - Dec.14 FINAL EXAM FINAL EXAM 8:00am-10:00am