Francis J. Narcowich, Professor

Narcowich ........ Wigner ......... Weisskopf

General Information

• Office: Blocker 611D
• Office hours: 12:30-1:30 MTWR, and by appointment.
• E-mail: fnarc@math.tamu.edu
• Phone: (979) 845-7554 (Messages only.)
• FAX: (979) 845-6028

Research Interests

• Approximation Theory and Mathematical Physics
• Curriculum Vitae
• Publications
• A First Course in Wavelets and Fourier Analysis, 2nd Edition, by Albert Bogess & Francis J. Narcowich

Education

• B.S. DePaul University 1968
• M.A. Princeton University 1970
• Ph.D. Princeton University 1972

Courses

Spring 2022

• Math 414-501: Fourier Series and Wavelets (BLOC 117, MWF 11:30-12:20)

  Information sheet

  Current homework. Due Tuesday, 5/3/2022.

  Previous assignments

  Schedule of presentations (10:30-12:30, May 10)

  Projects — Due Tuesday, May 10, by 4 pm.

  Notes

  Sine and cosine series

  Point-wise convergence of Fourier series

  Minimum residual energy and Parseval's Theorem

  Seismic trace

  Seismic trace and Fourier analysis

  Example: Chapter 4, Exercise 1

  Class notes for 4/22/22-5/2/22

  Matlab m-files

  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 L².)

  sampling_demo.m (Demonstrates the sampling theorem.)

  Test 1 review

  Test 1 review

  Practice Tests: 2002, 2003 and 2009

  Test 2 review

  Test 2 review

  Practice Tests: 2009 and 2010

  Test 3 review

  Test 3 review

  Practice Tests: 2002, 2009 and 2016

• Math 642-600: Analysis for Applications II (BLOC 117, MWF 10:20-11:10)

  Information sheet

  Bibliography

  Current homework. Due Wednesday, 4/13/2022

  Previous assignments

  Notes

  Fréchet and Gâteaux derivatives and the chain rule

  Isoperimetric Problem

  Lagrange Multipliers in the Calculus of Variations

  Sufficient conditions for an extremum

  Coordinates on the sphere

  The Courant-Fischer Theorem

  Laurent series example

  Exercises for complex variables

  Cauchy-Goursat Theorem. E. Croot, Georgia Tech.

  Graphs and Operators

  Tempered Distributions. Joel Feldman, University of British Columbia.

  Notes on Spectral Theory

  Notes on the Poisson Summation Formula