[Instructor: Christoph Ortner] [SYLLABUS] [PIAZZA]

Questions about the course should normally be posted on PIAZZA so that the entire group can benefit from the discussion. Please email the instructor only in exceptional circumstances, e.g. when an issue is clearly private.

Lectures and workshops are Tuesday 1400-1530 and Thursday 1400-1530. Normally, there will be lectures on Tuesdays and workshops on Thursdays, but there will be exceptions.

Note that you must have access to a Jupyter + Julia environment to complete the assignments. I will help you set this up. If you do not have access to personal computing equipment, please get in touch as soon as possible. I recommend working through WS01-WS01-Installing-Julia.ipynb on your own as soon as possible so you are set up.

Here I will post a brief summary of each lecture, the relevant notebooks, recordings etc.

No lecture due to Imagine Day.

• L01-Introduction.ipynb : introduction and motivation for the course
• L02-Preview-2ptBVP.ipynb : finite difference approximation of a 2-point boundary value problem, this provides a rapid overview of several concepts we will study in more detail throughout the course
• Recorded Lecture R01 Error Estimate for the 2-point BVP: [pdf], [mov], [m4v]

• L03-LinearSystems.ipynb : Numerical solution of linear systems, LU factorisation, review of eigendecomposition
• WS01-WS01-Installing-Julia.ipynb : setup of the computational infrastructure
• Recorded lecture R02 on hermitian matrices: [pdf], [mov], [m4v]

• Tue 22 Sep : L04, Nonlinear Systems
• Tue 29 Sep : L05, Interpolation and Quadrature
• Preparatory Reading: Intro to Fourier Analysis
  • recorded lecture
  • If you'd like to dive deeper into this topic I recommend e.g. Chapter 2 from Nick Trefethen's lecture notes.
• Tue 6, 13, 20 Oct : L06, L07, L08 on IVPs, Stability, Hamiltonian Systems
• Tue 27 Oct : PDEs - Diffusion
• Tue 3 Nov : PDEs - Advection
• Tue 10 Nov : PDEs - Fast solvers for elliptic problems
• Tue 17 Nov : Spectral methods - approximation theory
• Tue 24 Nov : Spectral methods - applications to PDEs
• Final Week of lectures : catch-up time