Project Title: Some alternative methods for numerical differentiation of certain monotonic functions.

Adviser: Steven From

Description: Most methods of numerically approximating the derivative of a function are based

upon polynomial interpolation and finite differences which are combined in a linear fashion.

We shall consider some alternative approaches to numerically differentiating a function which

is monotonic on some interval. These alternative approaches use some generalized notions

of means. We shall obtain theorems concerning when the new methods are superior to traditional

methods of numerical differentiation.

Prerequisites: Math 3230 required. Math 3300 recommended, but not required. A good understanding

of all three semesters of calculus and some basic Taylor series expansions is required along with

various representations of truncation errors and theorems of mean value type is needed. Also an understanding of how to solve some basic differential equations (some basics from Math 2350)