The fundamental problem. Extremals
The insufficiency of extremality
Important first integrals
The du Bois-Reymond equation
Legendre's necessary condition
Jocobi's necessary condition
Weak versus strong variations
Weierstrass's necessary condition
The transversality conditions
Hilbert's invariant integral
The fundamental sufficient condition
Jacobi's condition revisited
Necessary conditions for optimality
A singular control problem
A biological control problem
Optimal control to a general target
Navigational control problems
State variable restrictions
