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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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On the differentiation of a composite function with a generalized vector argument on homogeneous time scales; pp. 309–322

(Full article in PDF format) https://doi.org/10.3176/proc.2017.3.04


Authors

Vadim Kaparin, Ülle Kotta

Abstract

The paper proves a theorem on the differentiation of a composite function with a generalized vector argument. The theorem is formulated in terms of the delta derivative, which in the case of homogeneous time scales incorporates both the ordinary derivative and the difference operator. The term “generalized vector argument” implies that a composite function is allowed to depend not only on some variables but also on their delta derivatives. A formula in the theorem shows how the higher-order delta and partial derivatives of a composite function commute. Moreover, it enables reducing the order of the delta derivative, making computations simpler and more efficient. The computational efficiency of the formula was analysed on the basis of experiments in the symbolic computation software Mathematica.

Keywords

delta derivative, partial derivative, composite function, time scale calculus.

References

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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December