Институт математики и математического моделирования

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 56

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Date: Tuesday, February 17, 2026

Time: 14.00-15.00 (Istanbul) = 12.00-13.00 (Ghent) = 16.00-17.00 (Almaty)

Zoom link: https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDa VYrN3l5bzJVQT09 ,

Conference ID: 667 827 0445, Access code: 1

Speaker: Prof. Dr. Ali Uzer

Istanbul Arel University, Türkiye

Title: Multiplicative type complex calculus (MCC): a new analytical framework beyond classical calculus

Abstract: In this work, we introduce and analyze the framework of multiplicative type complex calculus (MCC) as an alternative to additive type complex calculus (ACC) within complex analysis. New definitions of differentiation and integration are formulated in the MCC setting and compared with their ACC counterparts. Multiplicative analogues of classical Taylor series expansions are derived, and their convergence properties are investigated. It is shown that, unlike ACC-based expansions, the MCC-based expansions yield non-divergent and numerically stable representations for a broad class of special functions. The applicability of MCC is further illustrated through the evaluation of integrals and series arising in wave propagation and scattering problems, where ACC formulations typically exhibit divergence or loss of accuracy. A systematic comparison between MCC and ACC reveals the analytical advantages of the multiplicative approach, including enhanced convergence behavior and robustness. These results demonstrate that MCC provides a consistent and effective analytical framework beyond ACC, with potential implications for complex analysis and applied mathematical modeling.

Biography:

Ali Uzer received the B.Sc., M.Sc., and Ph.D. degrees in Electrical Engineering from Gaziantep University, Turkey, in 1995, 1998, and 2005, respectively. He is currently a Professor in the Department of Electrical and Electronics Engineering at Istanbul Arel University, where he teaches courses on electromagnetics, signals and systems, and electrical machines. His research interests lie in analytical and semi-analytical methods for electromagnetic wave propagation, scattering, and diffraction, with particular emphasis on high-frequency techniques such as GTD, UTD, and PTD. He has made contributions to the application of multiplicative calculus and novel approximation techniques in electromagnetics.

Abstracts and forthcoming talks can be found on our webpage
https://sites.google.com/view/aam-seminars

Kazakh Mathematical Journal

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 56

Title: Multiplicative type complex calculus (MCC): a new analytical framework beyond classical calculus

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