Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Transcribed Image Text:Differentiability & Harmonics
State and prove the Cauchy-Riemann Theorem or Let ACC be an open set,
20 EA, and let f: AC where f = u + iv (u, v: R2R). Then f is analytic at
zo if and only there is a neighbourhood NCA of zo for which:
1. Juu, u, and
all exist and are continuous on N,
მემოყმე
2. The equations
ди
дх
av and u
=
ay
ay
მეს
, called the Cauchy-Riemann Equations,
are satisfied on all of N.
Moreover we have that f'(x + y) = u(x, y) + ix (x, y) = y(x, y) – idy (x, y).
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