Question 3 Let f(2) = u(z,y)+iv(z,y) be a complex function defined on some neighbourhood of zo = 10 + iyo- Assume further that • the partial derivatives uz, Uz, Uy and vy are all continuous at (x0,yo), and that • the Cauchy-Riemann equations hold at (z0,40). Prove that f is then differentiable at zo.
Question 3 Let f(2) = u(z,y)+iv(z,y) be a complex function defined on some neighbourhood of zo = 10 + iyo- Assume further that • the partial derivatives uz, Uz, Uy and vy are all continuous at (x0,yo), and that • the Cauchy-Riemann equations hold at (z0,40). Prove that f is then differentiable at zo.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 3
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Question 3
-) 'n komplekse funksie
wing van zo zo+iyo.
Let f(2) = u(z,y) + iv(x,y) be a complex function
defined on some neighbourhood of zo = 10 + iyo.
Assume further that
Uz, Uz, ly en vy almal
en dat
• the partial derivatives uz, Uz, Uy and vy are
all continuous at (ro,yo), and that
• the Cauchy-Riemann equations hold at
(20,40).
vergelykings geld by
eerbaar is by zo-
Prove that f is then differentiable at zo.
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