Differentiation in a new viewpoint
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CitationParsian, A. (2009). Differentiation in a new viewpoint. Maltepe Üniversitesi. s. 87.
In the theory of functions the domain of the differentiable functions needs to be locally connected and the derivative of a single variable function with variable x,for a particular value of x is a number given by the limh→0 f(x + h) − f(x) h Provided that this limit exists. This definition requires the values of the function f for all of the elements of its domain which are sufficiently near the point x.Here we introduce a new generalized form of the derivative definition in which the values of at most countably many points of the domain of the function near the x, i.e., the elements of a sequence which approaches to x,is needed, the situation which is hold with connivance in the region of all of sciences. Moreover this definition is done in such a way that all of the theorems of this theory are valid yet. First we generalized the concept of continuity of functions and show the validity of all of the theorems of this section of calculus and then use of them for extending the basic theory.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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