Dissertation/Thesis Abstract

Infinitesimal time scale calculus
by Cuchta, Tom, M.A., Marshall University, 2011, 93; 1492019
Abstract (Summary)

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.

Indexing (document details)
Advisor: Lawrence, Bonita A.
Commitee: Mummert, Carl, Sanyal, Suman
School: Marshall University
Department: Mathematics
School Location: United States -- West Virginia
Source: MAI 49/05M, Masters Abstracts International
Subjects: Mathematics
Keywords: Calculus, Difference equations, Differential equations, Dynamic equations, Infinitesimal, Time scale calculus
Publication Number: 1492019
ISBN: 978-1-124-62562-1
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