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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).

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).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 22E
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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).
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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