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Functional Analysis


Functional analysis and applications to spectral theory and partial differential equations.


Functional Analyis, Buhler, American Mathematical Society, 2018.


MATH 810 and MATH 820 or concurrent with MATH 820.

Credit Hours: 

The course will cover the following topics:

Hilbert and normed linear spaces, Banach spaces (Chapters 5 and 6, brief introduction.

Weak and Weak topologies on Banach spaces and applications to: divergence of Fourier series; Galerkin's method for solving PDE's and the representations of analytic functions with positive real part (Chapters 10, 11, and parts of 12).

Bounded linear operators (Chapter 15 and parts of 16).

Commutative Banach algebras and (analytic) functional calculus (Chapters 17, 18, 19).

Commutative symmetric operators in Hilbert space (Chapters 28, 29).

Spectral theory of symmetric, normal and unitary operators (Chapter 31) - properties of the spectrum, functional calculus and spectral resolutions.

(Stefanov 2020 )


Events Calendar

Using Math

CTE course transformation grant helps Emily Witt, assistant professor of math, develop active learning with student groups in calculus.  Positive results using modules developed with Justin Lyle and Amanda Wilkens, math graduate students, were attained.  Read more

Math and COVID-19: Sources on how math is being used to track the virus and its spread.  AMS link.

A mathematician-musician's breakthrough melds East, West. Read more.

Researcher's innovative approach to flood mapping support emergency management and water officials. Read more.

Nicole Johnson found a way to express her baton twirling using math. See video.