Physical Sciences and Mathematics Commons^™

Pursuing Analogies Between Differential Equations And Difference Equations, David L. Abrahamson

David L. Abrahamson

The study of ordinary differential equations has long been a staple in mathematics at both the undergraduate and graduate levels. Recently, instruction in the study of difference equations has widened, primarily due to the expanded role of the digital computer in mathematics. The two topics are inextricably linked at all levels, from elementary techniques through current research questions. Pursuing the analogies between these fields of study can only deepen the understanding of each. In particular, the study of many elementary topics in difference equations, requiring not even the use of calculus, can serve as a founda- tion for intuition and …