**MATFUII**

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, trigonometric functions.

*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 Equation.

**Requirements:**

MATFUI, especially calculus, optimization and linear algebra.

**Literature:**

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 some suggestions.

- 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 & Schwartz, Elsevier. - 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 optimization.

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.