Why bother with Differential Equations?

Here is a link to a modest pdf from Leigh Becker which does the best job I've found so far laying out the broad applicability of differential equations across all disciplines. Please read this before class:) The complete chapter is linked here if you are interested.

Constructing Differential Equations:

We are going begin by exploring how differential equations relate to feature of our lives as human beings in the 21st century. In each case you will be asked to go through a set of checks to help us generate a more grounded awareness of what the math is actually trying to tell us.

Those checks are:

Definition of useful variables and parameters

Dimensional analysis

Draft equation (check dimensions)

Determine constraints or boundary values

What are knowns and unknowns

We will first consider the mortgage payment problem and various models of population dynamics

Here are links to discussions (pdf's) by Michael Monagan (SImon Frazier U) and someone at the University of Wisconsin about the differential equation for mortages that informed the abuse I am going to heap on you.