Information for Spring 2025 MAE 289C: Functional Analysis

Contact:

• The class will meet T/Th 3:30-4:50 in 174 EBU2.

• Instructor: Prof. William McEneaney

  • Office hour: TBD, 1809 EBU1 (or just contact me to set up a time).
  • Office: 1809 EBU1.
  • Email: wmceneaney@ucsd.edu

Grading:

• We can discuss grading ideas, but my nominal plan is as follows.
• The grading would be based on the homework assignments and the take-home final.
• To obtain your numerical score, you would add all your scores from the homework assignments and take-home final, and then divide that number by the total possible sum of those scores. If you like, you may multiply that by 100 to obtain a standard percentage score.

Potential References (And no, I don't expect you to have all these!):

• H.L. Royden, Real Analysis (This contains a nice transition from real analysis to functional analysis.)
• E. Kreyszig, Introductory Functional Analysis with Applications (This uses an unusual equivalent definition of many spaces, but is a very readable text.)
• A.E. Taylor and D.C. Lay, Intro. to Functional Analysis (One of the classics of the field - a ``go to'' for me when I hit a tough issue.)
• R.F. Curtain and H.J. Zwart, An Intro. to Infinite-Dimensional Linear Systems Theory, Appendices Only!!! (The appendices have a truly excellent discussion of func. analysis, and are particularly useful if we discuss closed linear operators at length, where these are useful for D&C problems with PDE dynamics.)
• R. Adams, Sobolev Spaces (Chapter 3 (and some of the preceding material) is an excellent intro to Sobolev spaces, which we will likely use in some calculus of variations examples.)

• There has been some discussion wrt covering Brownian motion (Wiener measure), SDEs (stochastic diffl. eqs.) and the Feynman/Kac and Fokker/Plank equations. In that case, some of the course may shift from classical functional analysis to the above probabilistic analysis, and the following references would replace some of the above ones.
• B. Oksendal, Stochastic Differential Equations (A reasonably tractable discussion of SDEs and the more general context.)
• I. Karatsas and S.E. Shreve, Brownian Motion and Stochastic Analysis (More extensive, with more detail than that in Oksendal.)

Homework Assignments:

• Gradescope entry code: TBD

• Homework Assignment #1 is TBD.

Miscellaneous: