Introduction to the difference calculus through the Fibonacci numbers

Abstract

This note explores ways in which the Fibonacci numbers can be used to introduce difference equations as a prelude to differential equations. The rationale is that the formal aspects of discrete mathematics can provide a concrete introduction to the mechanisms of solving difference and differential equations without the distractions of the analytic conditions. Later the continuous analogues can be studied without the distraction of the symbolic apparatus which, in its own right, can be viewed as a tool of thought.