Qualitative Asymptotic Analysis of Complex Functions
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چکیده
Professional scientists and engineers frequently analyze problems with heuristic techniques to get crude solutions quickly without worrying about the details of mathematical justification and firm error estimates. The method of steepest descent is one such technique that is widely used to evaluate functions represented by complex integrals. Routine application of the method however requires the selection of an appropriate integration contour in the complex plane. The selection task, which is difficult to do analytically, is often accomplished by geometric reasoning about the singular points of the integrand. This paper presents an implemented program that captures this style of reasoning. The program is based on a contour selection heuristic that reformulates the task as a simple graph search. Combined with symbolic algebraic techniques, the contour selection heuristic allows the program to quickly find the leading term approximation to the integral when a parameter in the integral becomes large.
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