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This module uses the Maple computing language to teach: perturbation expansions, accelerated convergence, Padé approximations, asymptotic expansions, eigenvalue problems, and Green’s functions.

M820 Calculus of Variations and Advanced Calculus covers functionals, Gâteaux differential, Euler–Lagrange equation, First-integral, Noether’s Theorem, Second variation/Jacobi equation and Sturm–Liouville systems.

The theory of nonlinear ordinary differential equations is introduced with emphasis on geometrical aspects, approximation schemes and the determination of stability and periodicity of solutions.