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On an alternative view to complex calculus
Author(s) -
Bashirov Agamirza E.,
Norozpour Sajedeh
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4827
Subject(s) - mathematics , logarithmic derivative , calculus (dental) , algebraic number , several complex variables , logarithm , time scale calculus , fundamental theorem of calculus , algebra over a field , riemann surface , pure mathematics , multivariable calculus , mathematical analysis , holomorphic function , fundamental theorem , medicine , dentistry , control engineering , fixed point theorem , engineering
In most (if not all) textbooks on complex calculus, the differentiation and integration of complex functions are presented by using the algebraic form of complex variables because the respective formulae in terms of the polar form are inappropriate. In this paper, we demonstrate that by transferring the field structure of the system of complex numbers to the Riemann surface of complex logarithm and changing the sense of derivative and integral, complex calculus can be delivered in terms of the polar form of complex variables identically to the presentation in terms of algebraic form.