ODE / PDE
Ordinary and Partial Differential Equations — formal UofT coursework (MATB44, MATC46) covering both analytical techniques and Numerical Methods for solving them.
Courses: ODE (MATB44), PDE (MATC46)
Topics covered
- First- and second-order ODEs, systems, phase plane analysis
- Stability theory (Lyapunov, linearisation)
- Fourier series and eigenfunction expansions
- Heat equation, wave equation, Laplace/Poisson equations
- Method of characteristics; Green’s functions
Computational side
Numerical integration using SciPy (solve_ivp) and MATLAB (ode45). Modelled physical systems in Physics labs — damped oscillators, heat diffusion, wave propagation.
Related: Mathematics, Physics, Numerical Methods, SciPy