•  Fréchet and Gâteaux derivatives

•  differential geometry: geodesics

•  Plateau's problem: minimal surfaces

•  Lagrange multipliers

•  Weierstrass's E function: sufficient conditions for extrema

•  Sturm-Liouville problems

•  Hamilton's principle: classical mechanics

•  Noether's theorem: invariants and symmetries

•  continuum mechanics

•  Hamilton-Jacobi theory

•  quantum mechanics

•  numerical solutions: dynamic programming

•  problems in control theory

•  problems in biology

•  problems in architecture