Optimal Control
Topic	Notes (pdf)	Supplementary material
1. Introduction to dynamic optimization	Lecture 1
2. Differential equations	Lecture 2	Supplementary notes on Eigen values Nice Khan Academy video on eigenvalues
3. Introduction to optimal control	Lecture 3
4. Transversality conditions	Lecture 4
5. The intuition behind optimal control following Dorfman (1969) & the current value Hamiltonian	Lecture 5	Dorfman (1969) The meaning of lambda (video 11 minutes)
6. Lessons in the optimal use of natural resource from optimal control theory	Lecture 6	Hotelling (1931) Hartwick (1990)
13. Optimal control with constraints, bang-bang and most rapid approach path (MRAP) problems	Lecture 13
14. Stochastic control	Lecture 14
16. Numerical optimal control (not updated in a very long time)	Lecture 16
Numerical Dynamic Programming
7. Introduction to numerical dynamic programming (DP)	Lecture 7 Video of example	Video solving a DP problem with a circle and arrow diagram  Dreyfus, S. 2002. Richard Bellman on the Birth of Dynamic Programming. Operations Research 50(1):48-51.
8. A more formal introduction to dynamic programming	Lecture 8	Simple VB program and More complicated VB program
9. Markov processes and Burt & Allison 1963	Lecture 9	Burt & Allison (1963)
10. Examples of DP problems, Real Option Value and Quasi-Option Value	Lecture 10	VB solution to the American Put Option Problem Video walking through the Mensink & Requate example
11. Numerical Issues #1: The challenge of continuity	Lecture 11	Simple Spreadsheet to implement Newton’s Method
12. Numerical Issues #2: Acceleration methods	Lecture 12
15. Dynamic programming in econometric estimation	Lecture 15	Rust (1987) and Rothwell & Rust (1997)
16. Approximate Dynamic Programming		Powell (2007) especially chapter 4 (overview of ADP) Hull (2015) (short paper focused on methodological issues) Sprinborn and Faig (2018) (application with clear statement of methods)
Computer Programming Tutorials
Introduction to using Matlab’s symbolic algebra library	Matlab Tutorial
Programming using Visual Basic for Applications (VBA) with Microsoft Excel	VB Tutorial: