Notion of a virtual derivative

Details Notion of a virtual derivative Notion of a virtual derivative

2011-01-04

arxiv.org/abs/1101.0974v2

Nonlinear Analysis Modelling and Control (2011) vol.16, No.1, 116 - 123

Mathematics

General Mathematics

The diagrams are drown with the help of xy-pic and can be automaticly generated for the derivative of large degry of more gene

Scientific paper

Diagrams as a graphic expresion of derivatives is proposed for calculation of derivatives for composed function. The concret diagram is understood as a virtual derivative in contrast of concret derivative. In polynomial expression of functions derivative the concret derivative will be every monomic member, and the virtual derivative represent the sum of similar monomic members. The word virtual denotes that we dont need to know every virtual derivative, we don't write all the sequence of these virtual derivatives, and simply pick the needed one. This is in contrast of tradition to write the whole algebraic expresion as a denotion of whole function's derivative. Such graphic expresion can be helpful in the problems of differential geometry, in the various asymptotic expantions, also in the solution of some differential equations.

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