Exponential Approximations On Multiplicative Calculus
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A new kind of calculus, multiplicative calculus, was developed and the de…nition of a new kind of derivative was given within this calculus. Multiplication and division, in this calculus, take the role of summation and di¤erence in the ordinary calculus. Thus, multiplicative calculus is based on multiplicative rate of change, whereas the ordinary calculus is based on additive rate of change. In this manner, many functions can be represented by infinite product, analogous to the infinite sum, based on multiplicative derivative. These generate an idea for getting exponential approximations to functions.
Abstract
A new kind of calculus, multiplicative calculus, was developed and the de…nition of a new kind of derivative was given within this calculus. Multiplication and division, in this calculus, take the role of summation and di¤erence in the ordinary calculus. Thus, multiplicative calculus is based on multiplicative rate of change, whereas the ordinary calculus is based on additive rate of change. In this manner, many functions can be represented by infinite product, analogous to the infinite sum, based on multiplicative derivative. These generate an idea for getting exponential approximations to functions.
참고문헌 (4)
- Bashirov, A, "Multiplicative Calculus and its Applications", Journal of Mathematical Analysis and Applications, 337(1), pp.36~48 (2008)
- Grossman, M, "Non-Newtonian Calculus" (1972), Lee Press
- Stanley, D, "A Multiplicative Calculus", Primus, IX(4), pp.310~326 (1999)
- Kincaid, D, "Numerical Analysis", pp.1990, Brooks