Math 126 this Winter:

"Numerical analysis for PDEs and wave scattering"

This will cover modern integral-equation-based methods for solving
piecewise-constant coefficient PDEs (focusing on those arising in
electrostatics and time-harmonic waves), including the theory, analysis, and
coding experience required for proficiency. Much content will overlap with
previous Math 116's offered by Barnett. The prerequisites are some
programming experience (preferred: Matlab/octave, C, or fortran; esp. the
first). Recommended background includes some PDEs (could be at undergrad
level, eg Math 46), and real analysis (Math 63 and some graduate-level
functional analysis). However the background is flexible: a motivated
advanced undergrad or other science/engineering/CS student (undergrad or
grad) could pick up enough to learn a lot and do well.

We start with an introduction to numerical analysis, conditioning and
stability, numerical interpolation and integration, followed by potential
theory, Laplace's equation and Helmholtz equation. The latter leads to
scattering problems, a flavor of fast algorithms (FFT, fast multipole), and
final projects. Homework will be dominated by coding and implementing the
algorithms, but also include some proofs. Projects can be coding-based or a
deeper study of numerical analysis results.