On an alternative view to complex calculus

被引:9
作者
Bashirov, Agamirza E. [1 ,2 ]
Norozpour, Sajedeh [1 ]
机构
[1] Eastern Mediterranean Univ, Dept Math, Mersin 10, Gazimagusa, Turkey
[2] ANAS, Inst Control Syst, Baku, Azerbaijan
关键词
bigeometric calculus; complex logarithm; complex exponent; functions of complex variables; Riemann surfaces; GRADIENT;
D O I
10.1002/mma.4827
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:7313 / 7324
页数:12
相关论文
共 24 条
[11]  
Cordova-Lepe F., 2009, INT J MATH GAME THEO, V18, P527
[12]  
Cordova-Lepe F, 2006, TMAT REV LATINOAM CI, V2
[13]   Multiplicative Calculus in Biomedical Image Analysis [J].
Florack, Luc ;
van Assen, Hans .
JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2012, 42 (01) :64-75
[14]  
Grossman M., 1972, NONNEWTONIAN CALCULI
[15]  
Grossman M., 1983, Bigeometric Calculus: A System with a Scale-Free Derivative
[16]  
Kadak U., 2015, Abstr. Appl. Anal, V2015, P594685, DOI [10.1155/2015/594685, DOI 10.1155/2015/594685]
[17]   A non-Newtonian gradient for contour detection in images with multiplicative noise [J].
Mora, Marco ;
Cordova-Lepe, Fernando ;
Del-Valle, Rodrigo .
PATTERN RECOGNITION LETTERS, 2012, 33 (10) :1245-1256
[18]   Finite product representation via multiplicative calculus and its applications to exponential signal processing [J].
Ozyapici, Ali ;
Bilgehan, Bulent .
NUMERICAL ALGORITHMS, 2016, 71 (02) :475-489
[19]   On multiplicative and Volterra minimization methods [J].
Ozyapici, Ali ;
Riza, Mustafa ;
Bilgehan, Bulent ;
Bashirov, Agamirza E. .
NUMERICAL ALGORITHMS, 2014, 67 (03) :623-636
[20]   The Runge-Kutta method in geometric multiplicative calculus [J].
Riza, Mustafa ;
Aktore, Hatice .
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2015, 18 (01) :539-554