The Correlation Properties and Theorems of Backward Difference
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DOI: 10.25236/iccpb.2018.033
Author(s)
Wusheng Wang, Xuehua Ma
Corresponding Author
Wusheng Wang
Abstract
Difference is an important concept in calculus, which is widely used in mathematics, computer, engineering and ecology. This paper is made up of three parts: the first part is the introduction, which mainly introduces the current status of the research on the difference operation; the second part introduces the related properties and theorem about forward difference operation, including linear character, difference of the product , difference of quotient, the high order difference, Leibniz formula, discrete Rolle theorem, the difference mean value theorem, factorial power difference, discrete Taylor formula, etc; the third part is the result of the study, in which the properties and theorems of backward difference are obtained by analoging the basic properties and theorems of the forward difference, and the proof of them is given.
Keywords
Forward Difference, Backward Difference, Discrete Rolle theorem, Difference Mean Value Theorem, Discrete Taylor Formula