In Mathematical Economics I cover optimization theory starting with
the Lagrangean multiplier method. I also cover
economic dynamics using linear
differential and difference equations. This starts with cobweb models
of commodity markets and accelerator models of investment. It ends with
Pontryagin's Maximum Principle. Where my
course differs from others is
that I cover the methods of stochastic differential equations used in
financial economics. These methods are used in deriving such things as
the Black-Scholes Equationfor option value.
The solution to this differential equation gives the Black-Scholes Formula
for valuing stock options. The basis for this analysis is
Ito's Lemma for stochastic processes.
This material represents the use of mathematics in economics to
obtain practical results rather than for pure theory.