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MATH 464 , Fall 2012: Notes and Summary

 Lecture Date What was covered Notes Textbook Section 1 Aug. 30 Inroduction/Review of Analysis/Review of Linear Spaces with Scalar Product get assignment 1 1.1 2 Sept. 4 Review (cont.); Fourier Series - heat equation - 9.3 (548-553) 3 Sept. 6 Fourier series (I) turn in assignment 1 1.3 4 Sept. 11 Fourier series (II) turn in assignment 2 1.3 5 Sept. 13 Fourier series (III): L^2 theory; Plancherel theorem; mean square approximation error - 1.3, 1.5 6 Sept. 18 Fourier series (IV): pointwise convergence, Dirichlet criterion; Gibbs Phenomenon; Numerical Approximations Matlab code: convergence, Gibbs; turn in assignment 3 1.5 7 Sept. 20 Fourier transform: Definition, L2 theory - 1.5 8 Sept. 25 Rules for computing FT;sine-cosine transforms; convolutions; integral equations turn in assignment 4 3.1, 3.2; Problem 1.3 9 Sept. 27 Differential equations; Poisson Sum formula - 3.2 10 Oct. 2 Convolutions (1) turn in assignment 5 2.1,2.2, 2.3 11 Oct. 4 Convolutions (2) turn in assignment 6 1.2,2.3,2.4,3.3(153),4.2(193) - Oct. 5 REVIEW SESSION 3:00-5:00pm CSIC 4122 12 Oct. 9 TEST 1 - - 13 Oct. 11 Sampling of bandlimited signals; Sannon formula; reconstruction error (I) - 8.1, 8.2, 8.4 14 Oct. 16 Oversampling and reconstruction error (II) - 8.2, 8.4 15 Oct. 18 Reconstruction error (III); Generalized Function: Schwartz class of test functions - 8.4, 7.1 16 Oct. 23 Continuous and Slowly Growing (CSG) functions. turn in assignment 7 7.1 17 Oct. 25 Derivative of a distribution. Common generalized functions Class in CSI 1122 7.2 18 Oct. 30 Distributions: Derivative. Fourier transform CANCELED DUE TO HURRICANE SANDY see file 19 Nov. 1 Distributions: 1/x and Fourier transform turn in assignment 8 7.3 20 Nov. 6 Distributions: Convolutions, Algebraic and Ordinary Differential Equations Class in CSI 1122 7.3, 7.4 21 Nov. 8 Applications of Fourier transform to distributions; Periodic distributions Class in CSI 1122; turn in assignment 9 7.5, 7.7 - Nov. 9, noon TURN IN ASSIGNMENT 9 CSI 4131 - - Nov. 12 REVIEW SESSION 5:00pm-7:00pm CSIC 4122 22 Nov. 13 TEST 2 - - 23 Nov. 15 PDE: Wave Equation - 9.2 24 Nov. 20 PDE: Heat Equation (I) - 9.3 25 Nov. 22 No Class - Thanksgiving Break 26 Nov. 27 PDE: Heat Equation (II) - 9.3 27 Nov. 29 Windowed Fourier Transform (I) turn in assignment 10 11.2 , 11.3 , 11.4 28 Dec. 4 Windowed Fourier Transform (II)/Wavelet Transform (I) Here is some Matlab code. 11.4 29 Dec. 6 Wavelet Transform (II) - - 30 Dec. 11 Uncertainty Inequality; Instantaneous Frequency turn in assignment 11; Last Class -