- Systems of linear differential equations. Normal modes, natural oscillation frequencies.
- Double integrals, Jacobians. Line integrals, Green's theorem in the plane.
- Vector calculus: grad,div and curl; directional derivatives.
- Numerical solutions of ordinary differential equations. [Picard iteration.] Euler's Method. Runge-Kutta methods.
- Fourier Series.
- Partial Differential Equations (PDEs). Solution by separation of variables. Hyperbolic, elliptic and parabolic equations.
- Numerical solution of parabolic PDEs. Finite Difference Methods. [Solution of large numbers of sparse simultaneous equations.] Explicit and Crank-Nicolson methods, [Jacobi and Gauss-Seidel methods.]

[topics recently removed from the syllabus are included below in square brackets]