We hope to initiate a discussion about various methods for introducing Cauchy’s Theorem. Although Cauchy’s Theorem is the fundamental theorem upon which complex analysis is based, there is no “standard approach.” The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include Green’s Theorem, Goursat’s Lemma, Leibniz’ Rule, and homotopy theory, each of which has its positives and negatives.
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The definitive version is available at: https://www.tandfonline.com/doi/full/10.1080/10511970.2016.1234525?scroll=top&needAccess=true
Garcia, Stephan Ramon, and William T. Ross. "Approaching Cauchy’s Theorem." Primus 27, no. 8-9 (2017): 758-65. doi:10.1080/10511970.2016.1234525.
Garcia, Stephan Ramon and Ross, William T., "Approaching Cauchy’s Theorem" (2017). Math and Computer Science Faculty Publications. 219.