Introduction into Calculus over Division Ring
Abstract
Based on twin representations of division ring in an Abelian group I consider D vector spaces over division ring. Morphism of D vector spaces is linear map of D vector spaces. I consider derivative of function f of continuous division ring as linear map the most close to function f. I explore expansion of map into Taylor series and method to find solution of differential equation. The norm in D vector space allows considering of continuous mapping of D vector spaces. Differential of mapping f of D vector spaces is defined as linear mapping the most close to map f.
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