{"id":{"repo_id":"mo-state","oai_identifier":"oai:bearworks.missouristate.edu:theses-1853"},"canonical_url":"https://search.dev.ndltd.org/etd/mo-state/oai:bearworks.missouristate.edu:theses-1853","repository":{"repo_id":"mo-state","name":"Missouri State University","base_url":"https://bearworks.missouristate.edu/do/oai/"},"display":{"title":"The Other Calculus: a Survey of the Calculus of Finite Differences","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Shepard, Michael"],"institution":null,"degree_name":"Master of Science in Mathematics","degree_level":"Masters","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Les Reid"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1994,"date_issued":"1994-07-01T07:00:00Z","date_published":"1994-07-01T07:00:00Z","updated_at":"2026-07-24T03:15:54Z","subjects":["Mathematics"],"languages":[],"rights":["© Michael Shepard"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://bearworks.missouristate.edu/theses/852","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Les Reid"]},{"key":"dc:creator","label":"Author","values":["Shepard, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© Michael Shepard"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://bearworks.missouristate.edu/theses/852"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["The Other Calculus: a Survey of the Calculus of Finite Differences"]}]}],"canonical_facts":{"dc:contributor":["Les Reid"],"dc:creator":["Shepard, Michael"],"dc:description.abstract":["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."],"dc:identifier":["https://bearworks.missouristate.edu/theses/852"],"dc:rights":["© Michael Shepard"],"dc:subject":["Mathematics"],"dc:title":["The Other Calculus: a Survey of the Calculus of Finite Differences"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science in Mathematics"]},"updated_at":"2026-07-24T03:15:54Z"}