TL;DR
This paper develops the fundamental calculus theory for dual real numbers, establishing key theorems and extending classical calculus concepts into this algebraic framework.
Contribution
It introduces the basic calculus framework for dual real numbers and proves a fundamental theorem analogous to classical calculus.
Findings
Established calculus principles for dual real numbers
Proved the fundamental theorem of calculus in this context
Extended classical calculus to dual number algebra
Abstract
We present the basic theory of calculus on dual real numbers, and prove the counterpart of the ordinary fundamental theorem of calculus in the context of dual real numbers.
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Taxonomy
TopicsLogic, programming, and type systems · Mathematical and Theoretical Analysis · Numerical Methods and Algorithms