THE INTERVAL DERIVATIVE AND INTERVAL-DIFFERENTIAL CALCULUS - Levin, V. I. (Radio Electronics, Computer Science, Control, 2015)
The problem of the possible generalization of the classical differential calculus for functions with interval uncertainty of parameters is considered. In this regard, various types of uncertainty of function parameters and possible mathematical approaches to study of such functions are viewed. A detailed explanation of means of interval mathematics applied to study of functions with interval uncertainty of parameters is given. The concept of interval derivative is introduced by analogy with the classical notion of derivative of fully defined functions by passing to the limit. The theorem of existence of interval derivative is proved. Also we prove a theorem on representation of interval derivative through the original function. The interval derivatives of higher order are introduced and the theorem of existing of such derivatives if proved. Also we prove the theorem that allows us to represent derivatives of any high order through the original function. We derive an explicit expression for the interval derivative of any of order n as the interval the lower and upper limit of which are expressed in terms of boundaries of the original interval function. An example of use of interval derivative in the economy.