Teacher John Hassler
This course provides a mathematical preparation for, in
particular, the macro and the econometrics sequences. We will
cover the following topics
- Some Basics
- Integrals and integration, complex numbers,
- Difference and differential equations
- Some solution techniques for solving linear first and
higher order equations and systems of linear equations,
stability, linearizations and phase diagrams.
- Dynamic optimization
- Discrete and continuous time, optimal control
(Hamilton-Pontryagin) and dynamic programming (Bellman).
- Some numerical methods.
- Solving differential equations and maximization
problems. Possibly numerical solutions to the Bellman
MATFUI, especially calculus, optimization and linear algebra.
There is no required textbook for the course. There will be
handouts that will cover most of the material in the course.
However, you will most likely want to buy or at least have access
to a few books that will help you now and in the future. Here are
- A basic calculus book, covering a) Intergrals, b) Linerar
difference and differential equations, c) Complex
numbers, and d) Trigonmetric functions. A suggestion is Calculus,
K.G. Binmore, Cambridge University Press.
- A book on Optimal Control. Here I suggest Elements of Dynamic
Optimization, Alpha C. Chiang, McGraw. An
equivalent (but more expensive) alternative is Dynamic
Optimization: The Calculus of Variations and Optimal
Control in Economics and Management, Kamien &
- A book on Dynamic
Programming. I recommend A First Course in
Optimization Theory, R. K. Sundaram, Cambridge
Univeristy Press. In addition to a good introduction to
dynamic programminng, this book book also covers static
You may also find
lecture notes by previous teachers useful. Here are links to Harald Lang's and Paul Klein's notes. The latter give a deeper
and more formal treatement of many topics I will cover and is
strongly recommended for thoose who want a more solid foundation
for their mathematical skills.