JG Vargas: Real Version of Calculus of Complex Variable (II): Cauchy’s Point of View

by Jose G. Vargas (Submitted on 18 May 2012 to arxiv)

Abstract: As was the case in a previous paper, the differential form x+ydxdy plays the role that the variable z plays in the standard calculus of complex variable. The role of holomorphic functions will now be played by strict harmonic differential forms in the Kaehler algebra of the real plane. These differential forms satisfy the Cauchy-Riemann relations. No new concept of differentiation is needed, and yet this approach parallels standard Cauchy theory, but more simply. The power series and theorem of residues belong here at the end, unlike in the previous paper.

Download: http://arxiv.org/abs/1205.4256

Source: Email by Jose G. Vargas, josegvargas_at_earthlink.net, 22 May 2012.


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