Part 1

Part 2:

Lecture 9: Strong and weak minima. Jacobi's sufficient condition. (1/3, 2/3, 3/3)

Lecture 10: Weierstrass necessary condition. (1/3, 2/3 , 3/3)

Lecture 11: Weierstrass sufficient condition. (1/4, 2/4, 3/4, 4/4)

Suggested exercises.

Lecture 12: Hamilton-Jacobi theory, Bellman equation, Pontryagin maximum principle.  (1/2, 2/2)

Lecture 13: Jacobi's equation again, Jacobi condition and a field of extremals. Global minimum and convexity. (1/4, 2/4, 3/4, 4/4)

Lecture 14: Applications. (1/4, 2/4, 3/4, 4/4)