ABSTRACT
Recursion has been used to solve a wide variety of mathematical problems from ancient times to the present. This chapter examines diverse applications, many connected to previously covered topics, but please keep in mind the fact that finding a recursion isn’t always useful. In some cases no techniques exist for shortcutting it and the iterations can only presently be computed one at a time. Newton’s method is a technique used to approximate the roots of a differentiable function. The chapter begins with a guess, x0 and then calculates the tangent line to the curve at that point. Where this tangent line hits the x-axis is our next estimate. Then, the process is repeated to get third, fourth, fifth, etc. estimates. Euler had better luck with other difference equations. In fact, he was the one who came up with the characteristic equation method.
