Consider the region U = {r+yi € C: z>0, 00} be the upper half-plane. Find a conformal bijection f: U →V.
Consider the region U = {r+yi € C: z>0, 00} be the upper half-plane. Find a conformal bijection f: U →V.
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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Transcribed Image Text:1. Consider the region \( U = \{x + yi \in \mathbb{C} : x > 0, \ 0 < y < 1\} \). It is a sort of semi-infinite rectangle.
Let \( V = \{z \in \mathbb{C} : \text{Im}(z) > 0\} \) be the upper half-plane.
Find a conformal bijection \( f : U \to V \).
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