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Find ALL the analytic functions f(2)=u(x, y) +iv(x,y) defined on D = D = {z € C | |z| < 1} Vz= x+iye D. where 2u(x, y) — v(x, y) + 1 = 0 (Hint: Satisfying Cauchy Riemann Equation is a necessary but not sufficient condition for a function to be differentiable at a point. Being analytic at a point is different from being differentiable at a point. Being differentiable in a neighborhood containing a point is different from being differentiable at that point.)

Find ALL the analytic functions f(2)=u(x, y) +iv(x,y) defined on D = D = {z € C | |z| < 1} Vz= x+iye D. where 2u(x, y) — v(x, y) + 1 = 0 (Hint: Satisfying Cauchy Riemann Equation is a necessary but not sufficient condition for a function to be differentiable at a point. Being analytic at a point is different from being differentiable at a point. Being differentiable in a neighborhood containing a point is different from being differentiable at that point.)

Advanced Engineering Mathematics
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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Find ALL the analytic functions f(z) = u(x, y) +iv(x,y) defined on D = {z € C | |z| < 1} Vz= x+iy = D. where 2u(x, y) — v(x, y) + 1 = 0 (Hint: Satisfying Cauchy Riemann Equation is a necessary but not sufficient condition for a function to be differentiable at a point. Being analytic at a point is different from being differentiable at a point. Being differentiable in a neighborhood containing a point is different from being differentiable at that point.)
Transcribed Image Text:Find ALL the analytic functions f(z) = u(x, y) +iv(x,y) defined on D = {z € C | |z| < 1} Vz= x+iy = D. where 2u(x, y) — v(x, y) + 1 = 0 (Hint: Satisfying Cauchy Riemann Equation is a necessary but not sufficient condition for a function to be differentiable at a point. Being analytic at a point is different from being differentiable at a point. Being differentiable in a neighborhood containing a point is different from being differentiable at that point.)
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