Date of Award

2011

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Bonita A. Lawrence

Second Advisor

Carl Mummert

Third Advisor

Suman Sanyal

Abstract

Calculus has historically been fragmented into multiple distinct theories such as differential calculus, difference calculus, quantum calculus, and many others. These theories are all about the concept of what it means to "change", but in various contexts. Time scales calculus (introduced by Stefan Hilger in 1988) is a synthesis and extension of all the various calculi into a single theory. Calculus was originally approached with "infinitely small numbers" which fell out of use because the use of these numbers could not be justified. In 1960, Abraham Robinson introduced hyperreal numbers, a justification for their use, and therefore the original approach to calculus was indeed logically valid. In this thesis, we combine Abraham Robinson's hyperreal numbers with Stefan Hilger's time scale calculus to create infinitesimal time scale calculus.

Subject

Calculus

Subject

Differential calculus

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