![]() In the following subsections we narrow down the set of curves that we can integrate to include only those that can be built up out of a finite number of continuous curves that can be given a direction. This more precise definition allows us to consider what properties a curve must have for it to be useful for integration. ![]() This definition of a curve coincides with the intuitive notion of a curve, but includes a parametrization by a continuous function from a closed interval. A curve in the complex plane is defined as a continuous function from a closed interval of the real line to the complex plane: z : → C. In contour integration, contours provide a precise definition of the curves on which an integral may be suitably defined. In complex analysis a contour is a type of curve in the complex plane. ![]() One method can be used, or a combination of these methods, or various limiting processes, for the purpose of finding these integrals or sums. application of the Cauchy integral formula and.direct integration of a complex-valued function along a curve in the complex plane.One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods. Ĭontour integration is closely related to the calculus of residues, a method of complex analysis. In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.
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