Francis J. Narcowich, Professor

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

General Information

• Office: Blocker 611D
• Office hours: MTW 1-2, and by appointment.
• E-mail: f-narcowich@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 Boggess & Francis J. Narcowich

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Education

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

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Courses

Fall 2025

• Math 641-600: Analysis for Applications I (Room BLOC 121)

  Information sheet

  Additional References

  Current homework. Due 11/19/2025

  Previous assignments

  Keener's missing pages: 140 & 141

  Midterm

  Date: Wednesday, October 15, 2025

  Midterm review

  Class Notes

  Vector spaces

  Inner products and norms

  Coordinates and bases

  Diagonalization

  Adjoints, self-adjoint operators, spectral theory, Courant-Fischer theorem, Fredholm alternative

  Banach spaces and Hilbert spaces

  Lebesgue integration

  Orthonormal sets and expansions

  Approximation of continuous functions

  Pointwise convergence of Fourier series

  Discrete Fourier transform

  Splines and finite element spaces

  X-ray tomography and integral equations

  Bounded operators and closed subspaces

  The Projection Theorem, the Riesz Representation Theorem, Adjoints, and the Fredholm Alternative

  An example of the Fredholm alternative and finding a resolvent

  Compact operators

  The Closed Range Theorem

  Spectral theory for compact operators

  Neumann Expansions

  Example problems for distributions

Previous Semesters

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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

August 2024

Applied Analysis Part

Numerical Analysis Part

January 2025

Applied Analysis Part

Numerical Analysis Part

August 2025

Applied Analysis Part

Numerical Analysis Part

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