Welcome to the public homepage of Math F617 Functional Analysis, Spring 2026, in the Dept. of Mathematics and Statistics at the University of Alaska Fairbanks.

Instructor: Ed Bueler

Email me at elbueler@alaska.edu. I hold office hours in Chapman 306C.

Content (Mission Statement)

I plan to teach this functional analysis course as though it is in support of applied mathematics, and specifically of the finite element method. Each week I will start with an applied or numerical computation of some kind, and then spend the rest of the week gathering the functional analytic definitions and theory to support it. Note that infinite-dimensional normed vector spaces, especially Hilbert and Banach spaces, are the central objects of functional analysis. The solutions of continuum problems like partial differential equations live in such spaces. Generally these spaces contain functions on domains in R^d, d=2,3, with some regularity to allow derivatives and boundary values; often they are Sobolev spaces. Such spaces contain high-quality approximating finite-dimensional subspaces, namely piecewise-polynomial spaces of the finite element method and also the trigonometric subspaces of Fourier analysis. Note that this course is not primarily about finite element calculations themselves, and programming will not be an essential skill. However, linear functionals, Sobolev spaces, integral operators, differential operators, bilinear forms, and interpolation will all be important ideas.

We will have to see if this course structure works! It is experimental.

Signing-up

Please sign up for the in-person “901” section (crn 35010), and plan to attend lecture in Chapman 107.

Canvas course page

Log in to canvas.alaska.edu/courses/30068 for the lecture Zoom link, Homework and Exam solutions, and to see your grades.

Getting Started

• Get a copy of the textbook, K. Saxe, Beginning Functional Analysis, Undergraduate Texts in Mathematics, Springer 2010.

• Attend lectures: MWF 10:30-11:30am in Chapman 107, or online.

• Read the Syllabus (PDF).

• The Schedule (PDF) has exam dates and homework due dates.

• The daily log has the recent happenings, including slides and worksheets as PDFs, and some planned material.

• Check out the nearly-weekly homework Assignments.

• There are three Exams: two Midterms and a Final. All are in class, and the Final will happen at the scheduled time. See the Exams tab for review guides.

           

• What are we studying? Check out these Wikipedia pages for the topics we plan to touch:

  • functional analysis
  • Hilbert spaces
  • Banach spaces
  • Sobolev spaces
  • Fourier series
  • approximation theory
  • bounded operators
  • partial differential equation
  • boundary value problems
  • finite element method

• Videos which might help with “getting started”:

  • abstract vector spaces (3Blue1Brown)
  • Fourier series (3Blue1Brown)
  • partial differential equation (3Blue1Brown)
  • compactness
  • Lebesgue integral

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Site design derived from coordinated Calc I, an original Jekyll design by David Maxwell.