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单词 contour integration
释义

contour integration

A contour integral is a path integral ∫C f(z) dz of a function f in the complex plane along an oriented, usually closed curve C. Such integrals can be evaluated using Cauchy's Residue Theorem; using appropriately chosen contours and integrands, and then taking real or imaginary parts, a vast range of integrals and series can be determined. For example, the substitution z = e changes the integral inline into the path integral inline where C is the positively oriented unit circle centred at 0. The new integrand has a double pole inside C, the residue of which can be determined and so the integral evaluated.

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更新时间:2025/5/20 8:42:53