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A Shortcut to the Cauchy Integral TheoremDecember 2024
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88 Reads
This paper introduces a concise pedagogical approach to prove the Cauchy-Goursat theorem for simply connected domains, avoiding the use of the Cauchy-Riemann equations. We establish this theorem for arbitrary closed curves within simply connected domains, relying only on the result for rectangles. Additionally, we present an analogous proof of the Cauchy integral formula in the same setting. R𝐞𝐜𝐨𝐦𝐦𝐞𝐧𝐝𝐞𝐝 𝐟𝐨𝐫 𝐭𝐞𝐚𝐜𝐡𝐢𝐧𝐠 𝐢𝐧 𝐮𝐧𝐝𝐞𝐫𝐠𝐫𝐚𝐝𝐮𝐚𝐭𝐞 𝐚𝐧𝐝 𝐩𝐨𝐬𝐭𝐠𝐫𝐚𝐝𝐮𝐚𝐭𝐞 𝐜𝐨𝐦𝐩𝐥𝐞𝐱 𝐚𝐧𝐚𝐥𝐲𝐬𝐢𝐬 𝐜𝐨𝐮𝐫𝐬𝐞𝐬!
