Francis Narcowich
Francis J. Narcowich, Professor
Narcowich ........
Wigner ......... Weisskopf
General Information
 Office: Blocker 611D
 Office hours: MW 12, F 121 and by appointment.
 Email: fnarcowich@tamu.edu
 Phone: (979) 8457554 (Messages only.)
 FAX: (979) 8456028
Research Interests
Education
 B.S. DePaul University 1968
 M.A. Princeton University 1970
 Ph.D. Princeton University 1972
Courses
Spring 2024

Math 414501: Fourier Series and Wavelets (BLOC 164, MWF
33:5)

Information sheet

Current homework. Due 4/22/24.

Previous assignments

Projects — Due Wednesday, May 1, by 5 pm.
 Notes

Lebesgue
integration

Least squares

Sine and cosine series
 Pointwise
convergence of Fourier series

Minimum residual energy and Parseval's Theorem

Seismic trace

Seismic trace and Fourier analysis (Shows the trace plus
Fourier analysis
 Example: Chapter 4, Exercise 1
 Positivity property
for an inner product derived from a matrix
 The relationship
between the Fourier series for $f$ and $f'$
 Notes for Feb. 23,
2024

Discrete Fourier transform

Example 4.11: Decomposition

Example 4.11: Reconstruction
 Matlab mfiles
 Matlab
Basics, by Professor Peter Howard

part_sum_c.m
(Partial sums of FS, given the coefficients)

part_sum.m
(Computes the partial sum of a function.)

dir_kern.m
(Dirichlet/Fourier kernel.)

pieces.m (Plots a function with jump discontinuities)

mean_FS.m (Demonstrates convergence of Fourier series, both
uniformly and in L^{2}.)

sampling_demo.m (Demonstrates the sampling theorem.)
 Test 1

Test 1 review
 Links to practice
tests:
2002, 2009
and 2015
 Test 2

Test 2 review
 Links to practice
tests:
2012,
2014
Applied Analysis/Numerical Analysis Qualifiers

Applied/Numerical Qualifier Syllabus
 May 2006
 January 2007
 May 2007
 May 2008
 January 2009
 August 2009
 January 2010
 August
2010
 January
2011
 August
2011
 January
2012
 August
2012
 January
2013
 August
2013
 January 2014
 Applied Analysis Part
 Numerical Analysis
Part
 August 2014
 Applied Analysis Part
 Numerical Analysis
Part
 January
2015
 August 2015
 January 2016
 August 2016
 August 2017
 January 2018
 August 2018
 Applied Analysis Part
 Numerical Analysis
Part
 January 2019
 Applied Analysis Part
 Numerical Analysis
Part
 August 2019
 Applied Analysis Part
 Numerical Analysis
Part
 January 2020
 Applied Analysis Part
 Numerical Analysis
Part
 August 2020
 Applied Analysis Part
 Numerical Analysis
Part
 January 2021
 Applied Analysis Part
 Numerical Analysis
Part
 August 2021
 Applied Analysis Part
 Numerical Analysis
Part
 January 2022
 Applied Analysis Part
 Numerical Analysis
Part
 August 2022
 Applied Analysis Part
 Numerical Analysis
Part
 January 2023
 Applied Analysis Part
 Numerical Analysis
Part
 August 2023
 Applied Analysis Part
 Numerical Analysis
Part
January 2024
 Applied Analysis Part
 Numerical Analysis
Part
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