A MATLAB-based visualization package for complex functions, and their mappings and integrals


This paper aims to supply a tutorial on the visualization of advanced functions. The MATLAB-based mostly package ComplexGUI was prepared to illustrate mappings by elementary complex functions. The tool shows how user-defi ned curves and regions are remodeled by some elementary functions. Ideas like branch points, branch cuts, the principal branch of multivalued functions, and Riemann surfaces are emphasised. The package additionally enables asymptotic analysis of Bessel integrals along user-specifi ed contours, and compares the result with the engineered-in perform in MATLAB. The tool allows deforming the mixing contour to a path through the saddle points within the direction of the steepest-decent path to obtain a higher result.

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