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Conference publicationsAbstractsXXII conferenceInterval Derivative and Modelling of Systems in Condition of UncertaintyRussia, 440039, Penza, Baidukova pr., 1-a, PenzGTU 1 pp. (accepted)We will use the algebra of interval numbers. Operands in it - closed real intervals. Operations on how to introduce set-theoretic generalization operations on real numbers:. Ie can introduce operations on intervals. Interval function - one mapping of the same type on the set, where - interval independent variable - dependent variable interval - Interval function. Say that an unbounded interval approaches the limit when approaching indefinitely, and to. Ie .:. Similarly, the dependent variable interval function can be arbitrarily close to the limiting interval, ie, . If unlimited unlimited due to the approximation approach to, say, that the limit of the function at present, ie, . If the interval is continuous, ie, lower and upper bounds - continuous functions of the lower and upper bounds, then. Consider a continuous interval function. We fix the value of the independent variable. This value because of the continuity, the corresponding fixed value. Increments of independent and dependent variables relative to their fixed values:. Form the ratio of the second to the first increment. Take it with unbounded limit approaching its fixed value:. This limit will be called the interval, and denote the derivative or. Theorem 1. In order that existed at the interval derivative of the gap function, it is necessary and sufficient that in some neighborhood of this point, including herself, all the values of a variable are non-degenerate intervals. Theorem 2. Interval derivative of the continuous interval function can be expressed in the final form. The derivative of the interval function is also a function of the interval. This allows you to continue the process by first obtaining the second derivative, then the third derivative, etc.
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