PHY330 — Numerical methods for physics & engineering.
A hands-on introduction to the numerical methods that underpin modern computational physics — linear algebra, root-finding, interpolation, integration, ODEs/PDEs, and a survey of stochastic methods.
Numerical linear algebra
Direct and iterative solvers, conditioning and stability, eigenvalue problems — building intuition through coded examples in Python and NumPy.
Root-finding, interpolation, integration
Bisection, Newton, secant; polynomial and spline interpolation; Newton-Cotes and Gaussian quadrature. Convergence and error analysis sit alongside the recipes.
ODEs & PDEs
Initial- and boundary-value problems. Explicit, implicit, and symplectic integrators. Finite-difference and finite-element treatments of canonical PDEs (heat, wave, Poisson).
Stochastic methods
Monte Carlo integration, Markov-chain Monte Carlo, basic SDEs — a short tour of probabilistic computation applied to physics.