Course Project: AMATH-732 Asymptotic Analysis and Perturbation Theory
Course Description
Graduate course on asymptotic and perturbation methods, with emphasis on regular/singular perturbations, multiple scales, resonance, boundary layers, and WKB. Maple and Matlab are used alongside analysis.
Lab Book
Selected topics:
- Padé approximation and rational extrapolation of asymptotic series
- Fourier/spectral methods for oscillatory systems
- Mathematical oncology model of drug-resistance dynamics
Final Oral Presentation
Normal modes of N coupled oscillators: governing equations, a general procedure for obtaining all mode frequencies, and an explicit four-oscillator example with mode shapes.
Conclusion: the spectrum follows from the tridiagonal coupling matrix; frequency spacing is determined by coupling strength and boundary conditions.