SIX MORE ADVANCED TOPICS IN NUMERICAL ANALYSIS

Prof. Nick Trefethen, Fall 2018

Tuesdays at 1:25pm in CIWW 512 (usually)

This six-week course will be structured in an unusual way, following the pattern of last year's course but with new topics. Each of our six meetings will be independent. At each meeting, the first hour will be a lecture aimed at anyone interested in numerical analysis at a high level, organized around a well-known topic and mixing historical perspectives, recent developments, and always some new mathematics. The second hour will be for enrolled students only, a hands-on work session making use of Matlab and/or Chebfun. In the final two weeks each student will complete a small project.

The following tentative schedule of topics is not yet finalized:

  • Lecture 1, 04 Sep: Series solutions of Laplace problems
  • Lecture 2, 11 Sep: Pseudospectra
  • Lecture 3, 18 Sep: Block operators and spectral discretizations
  • Lecture 4, 25 Sep: Exponential integrators for stiff PDE
  • Lecture 5, 02 Oct: Minimax, CF, and Hankel norm approximation
  • Lecture 6, 09 Oct: Polynomials and multivariate polynomials
    • Note: this lecture will take place in CIWW 1314.
  • [Possible alternative topic: Contour integrals and hyperfunctions]

For reference, here are last year's topics (Fall 2017):

  • Lecture 1, 2017: Gaussian elimination
  • Lecture 2, 2017: Random functions and random differential equations
  • Lecture 3, 2017: Chebyshev series
  • Lecture 4, 2017: Rational functions
  • Lecture 5, 2017: Quadrature
  • Lecture 6, 2017: ODEs