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Complex Integration and Cauchy’s Theorem
1997In the last chapter we extended differentiation to complex functions. We now move on to an appropriate theory of complex integration. From this theory we will be able to give our second proof of the Fundamental Theorem of Algebra.
Benjamin Fine, Gerhard Rosenberger
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Cauchy’s Integral Theorem. Proof of Theorem 3.1. Cauchy’s Integral Formula
2017We will now give further applications of Theorem 9.1. In what follows we often consider functions holomorphic on domains containing the closure \( \overline{D} \) of a domain D. For such a function f we write \( f \in H(\overline{D})\).
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On Goursat's Proof of Cauchy's Integral Theorem
The American Mathematical Monthly, 2008(2008). On Goursat's Proof of Cauchy's Integral Theorem. The American Mathematical Monthly: Vol. 115, No. 7, pp. 648-652.
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The homotopic proof of Cauchy's integral theorem
International Journal of Mathematical Education in Science and Technology, 1980The object of this paper is to present a simple proof of the homotopic version of Cauchy's integral theorem which requires only the definition of integral over a piecewise continuously differentiable path, and which is constructive in the sense that it follows the deformation of one path onto another ‘across’ the homotopy.
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Complex Integration: Cauchy’s Theorem
1997Abstract In the last few chapters our efforts to extend the idea of differentiation to complex mappings have been amply rewarded. By innocently attempting to generalize the real derivative we were quickly led to the amplitwist concept, and the subject then came to life with a character all its own. While many of the results cast familiar
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The Gauss-Green and Cauchy Integral Theorems
The American Mathematical Monthly, 1975(1975). The Gauss-Green and Cauchy Integral Theorems. The American Mathematical Monthly: Vol. 82, No. 6, pp. 625-629.
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