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Search results with tag "Complex integration"
4. Complex integration: Cauchy integral theorem and …
www.math.hkust.edu.hkCauchy integral theorem Let f(z) = u(x,y)+iv(x,y) be analytic on and inside a simple closed contour C and let f′(z) be also continuous on and inside C, then I C f(z) dz = 0. Proof The proof of the Cauchy integral theorem requires the Green theo-
Complex integration - University of Arizona
www.math.arizona.edu1.3 Complex integration and residue calculus 1.3.1 The Cauchy integral formula Theorem. (Cauchy integral formula) Let f(ξ) be analytic in a region R. Let C ∼ 0 in R, so that C = ∂S, where S is a bounded region contained in R. Let z be a point in S. Then f(z) = 1 2πi Z C f(ξ) ξ −z dξ. (1.31) Proof: Let Cδ(z) be a small circle about z ...