A MATLAB-Based Visualization Package for Complex Functions, and their Mappings and Integrals

被引：4

作者：

Uluisik, Cagatay ^{[1
]}

Sevgi, Levent ^{[1
]}

机构：

[1] Dogus Univ, Elect & Commun Engn Dept, TR-34722 Istanbul, Turkey

来源：

IEEE ANTENNAS AND PROPAGATION MAGAZINE | 2012年 / 54卷 / 01期

关键词：

Functions of a complex variable; conformal mapping; mapping by elementary functions; branch point; branch cut; principal branch; multivalued functions; Riemann surfaces; complex integration; Bessel functions; saddle point; steepest decent path (SDP); contour deformation; visualization; MATLAB; graphical user interface (GUI);

D O I：

10.1109/MAP.2012.6209520

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

This paper aims to provide a tutorial on the visualization of complex functions. The MATLAB-based package ComplexGUI was prepared to illustrate mappings by elementary complex functions. The tool shows how user-defined curves and regions are transformed by some elementary functions. Concepts such as branch points, branch cuts, the principal branch of multivalued functions, and Riemann surfaces are emphasized. The package also enables asymptotic evaluation of Bessel integrals along user-specified contours, and compares the result with the built-in function in MATLAB. The tool allows deforming the integration contour to a path through the saddle points in the direction of the steepest-decent path to obtain a better result.

引用

页码：243 / 253

页数：12

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