The Other Calculus: a Survey of the Calculus of Finite Differences

The Calculus of Finite Differences is a fascinating field of mathematics which is easily accessible to an undergraduate mathematics major. This paper attempts to present a broad survey of results from this field which show its richness, without appealing to deep results in analysis. Topics covered include differences, sums, factorial powers, approximation, and difference equations. An emphasis is given to the powerful Euler-Maclaurin sum formula because of its ability to connect differential and difference calculus and provide insight into asymptotic relationships. The paper includes comments on each section which point to deeper studies for those interested.

Name thesis:degree_name

Master of Science in Mathematics

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Mathematics

Year

1994

Author dc:creator

• Shepard, Michael

Contributors dc:contributor

• Les Reid

• Mathematics

Statement dc:rights

• © Michael Shepard

Repository record dc:identifier

https://bearworks.missouristate.edu/theses/852

OAI identifier oai:identifier

oai:bearworks.missouristate.edu:theses-1853