Introduction; 1. Integrals of the first order: maxima and minima for special weak variations: Euler test, Legendre test, Jacobi test; 2. Integrals of the first order: general weak variations: the method of Weierstrass; 3. Integrals involving derivatives of the second order: special weak variations, by the method of Jacobi; general weak variations, by the method of Weierstrass; 4. Integrals involving two dependent variables and their first derivatives: special weak variations; 5. Integrals involving two dependent variables and their first derivatives: general weak variations; 6. Integrals with two dependent variables and derivatives of the second order: mainly special weak variations; 7. Ordinary integrals under strong variations, and the Weierstrass test: solid of least resistance: action; 8. Relative maxima and minima of single integrals: isoperimetrical problems; 9. Double integrals with derivatives of the first order: weak variations: minimal surfaces; 10. Strong variations and the Weierstrass test, for double integrals involving first derivatives: isoperimetrical problems; 11. Double integrals, with derivatives of the second order: weak variations; 12. Triple integrals with first derivatives; Index.
