Lecture Timeline · PHY622

Mathematical Methods in Physics II, in teaching order (semester 2, one 3-hour lecture per week). Three arcs: calculus of variations → complex analysis → group theory.

Lecture	Arc	Topics	Wiki pages
Lec 1	Variations	Functionals, Euler–Lagrange equation, geodesics, minimal surfaces, constraints	Calculus of variations · Euler–Lagrange · Geodesics · Minimal surfaces · Lagrange multipliers · E–L equation (eq.) · Geodesic curvature (eq.)
Lec 2	Variations	Hamilton's principle — mechanics from a variational principle	Hamilton's principle
Lec 3	Complex	Complex numbers, analytic functions, Cauchy–Riemann conditions	Complex numbers · Analytic functions · Cauchy–Riemann · C–R equations (eq.)
Lec 4	Complex	Contour integration: Cauchy's theorem & integral formula, residues, conformal maps	Contour integration · Cauchy's theorem · Integral formula · Residue theorem · Conformal mapping · Residue formula (eq.) · Conformal map explorer
Lec 5–6	Complex	Applications: real integrals by residues, physics uses	Residue theorem · Conformal mapping
Lec 7	Groups	Symmetry groups: definitions, examples, subgroups	Symmetry groups
Lec 8–9	Groups	Group representations, characters	Group representations
Lec 10–11	Groups	Lie groups and Lie algebras	Lie groups · Lie bracket (eq.)
Lec 11–12	Groups	SU(2), SO(3) and spin — the physicist's payoff	SU(2) ↔ SO(3)

Where the arcs lead

Variational calculus becomes Lagrangian mechanics and field theory; contour integration powers every Green's function and dispersion relation (see Landau damping for a spectacular physics application of contour deformation); group theory is the grammar of quantum mechanics and particle physics.