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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2010 • Question 9

Question

Math 6210 • Real Analysis Spring 2010 • Question 9

Find all conformal transformations \(f(z)\) from the upper half disc \[ \{z\mid |z|<2 \text { and } \operatorname {Im}z>0\} \] onto the unit disc \(\{z\mid |z|<1\}\) such that \(f(i)=0\).

Raw LaTeX

Find all conformal transformations \(f(z)\) from the upper half disc
\[
\{z\mid |z|<2 \text{ and } \operatorname{Im}z>0\}
\]
onto the unit disc \(\{z\mid |z|<1\}\) such that \(f(i)=0\).

Topic Tags

Conformal Moduli and Annuli Riemann Mapping Theorem and Simply Connected Domains