Topics in applied analysis

• Asymptotic integrals: part 1, part 2
• Shallow wave theory
• Traffic model See also sample FlexPDE script for Burger eqn
• GM model:
  • Spike patterns in GM system 1: introduction
  • Dynamics of a single interior spike in the GM system
  • Spike patterns in GM system 2: Wei's proof of stability of NLEP problem
  • Spike patterns in GM system 3: Stability of K spikes, large and small eigenvalues
  • FlexPDE scripts: Dynamics of a single interior spike | two interior spikes | two boundary spikes
• Travelling waves in thin domains
  • See the FlexPDE script front1d.pde
• Metastability: exponentially slow motion of interfaces in 1D Allen-Cahn model
  • See the FlexPDE script front1d-two.pde
• MEMS modelling
• Turing instability
• Using multiple scales to get a Complex Ginzburg Landau PDE from a PDE with a delay
• Method of multiple scales applied to Rayleigh oscillator

• My notes on various topics
• See also notes from last time class was offered
• PPlane software

• hw1 Download maple worksheet for Rayleigh oscillator from here.
  • Solution to q2d on hw1
• hw2 Sample FlexPDE file here
• hw3 Sample FlexPDE file here
• hw4 See sample FlexPDE above for GM model
• hw5 See sample FlexPDE above for Burger eqn
• hw6

Term project:
For term project, you will be required to read a mutually agreed upon research paper, give an in-class presentation on it, and submit a report. More information will be given during the class.