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

I plan to teach this functional analysis course as though it is in support of the finite element method. Each week I will start with a 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, including Hilbert and Banach spaces, are central to functional analysis. The exact solutions of continuum problems like partial differential equations live in such spaces. Generally these are spaces of functions on domains in euclidean space, with some given regularity to allow derivatives and boundary values, so they are often Sobolev spaces. These spaces also contain high-quality approximating finite-dimensional subspaces, such as the piecewise-polynomial spaces of the finite element method. This course is not really about finite element calculations themselves, and programming will not be an essential skill, but linear functionals, bilinear forms, Sobolev spaces, and interpolation will be important ideas.

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

Signing-up

If you plan to be present on campus in Fairbanks during the semester, please sign up for the in-person “901” section (crn 35010), and plan to attend lecture in Chapman 107. If you are remote, signing up for the web-based “701” section (crn 35018) is just fine!

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) is my longer-term plan. Check it for exam dates and due dates, and for which topics come next!

• The daily log has the recent happenings, including handouts and worksheets as PDFs.

• Check out the nearly-weekly homework Assignments.

• There are three Exams, two Midterm Quizzes 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.