Math 534 FINAL: THEORETICAL QUESTIONS Autumn 2007
1. Normal convergence, normal limit of analytic functions is analytic.
2. Set of convergence for a power series, Cauchy-Hadamard Theorem.
3. Power series expansion for analytic functions.
4. Theorem on isolated zeros of analytic functions.
5. Open Mapping Theorem.
6. Schwarz’s Lemma.
7. Invariant form of Schwarz’s Lemma.
8. Uniqueness Principle and principle of permanence of functional equation.
9. Laurent decomposition.
10. Laurent series expansion.
11. Classification of singularities and Riemann’s Theorem on removable singular-
ities.
12. Classification of singularities and theorems about poles.
13. Classification of singularities and the Casorati-Weierstrass Theorem.
14. Meromorphic functions and partial fractions decomposition.
15. Series expansion of functions periodic and analytic in a strip.
16. Residue Theorem.