This mathematical physics course aims to be an introduction to differential equations. Besides standard topics in ordinary and partial differential equations, nonlinear dynamical systems will be studied and nonlinear ODEs will be analysed using geometric and computational tools.
Recommended course content:
Ordinary differential equations: First order equations, integrating factors. Second order equations. Frobenius and other methods, singular points. Special Functions (Legendre, Bessel, Hermite, Laguerre). Fourier series.
Partial differential equations: Laplace’s equation, classical wave equation, diffusion equation.
Dynamical systems: Nonlinear ODEs. Flows and vector fields, phase space analysis.
Pre-requisites: Mathematical Physics I (Mathematical and Computational Toolkit).
Taught at the level of: Differential Equations with Applications and Historical Notes (G F Simmons), Nonlinear Dynamics and Chaos (S Strogatz).
amin.nizami@ashoka.edu.in