TRINITY COLLEGE DUBLIN
Complex Analysis for JS & SS Mathematics, SS Twosubject
moderatorship
Course 414 (lecturer: Richard M. Timoney)
Topics
There is a syllabus
in the
online course
descriptions at
http://www.maths.tcd.ie/pub/official/CoursesNow.
Notes
 Notes for Chapter 0 (on basic ideas about open, closed, connected
and compact sets in the complex plane and on the definition of
continuity) can be found here as a pdf
file.
 Notes for Chapter 1 (on some fundamentals of complex analysis,
definition of analyticity, CauchyRiemann equations, power series,
Cauchy's theorem and formula for a convex set, other versions of
Cauchy's theorem)
can be found here as a pdf
file.
 Notes for Chapter 2 (on simple connectedness,
logarithms, existence of global antiderivatives)
can be found here as a pdf
file.
 Notes for Chapter 3 (on the identity theorem and the maximum
modulus theorem) can be found here as a pdf
file.
 Notes for Chapter 4 (on the residue theorem,
open mapping theorem, removable singularities) can be found here as a pdf
file.
 Notes for Chapter 5 (on H(G) as a metric space)
can be found here as a pdf
file.
 Notes for Chapter 6 (on M(G) as a metric space and normal
families)
can be found here as a pdf
file.
 Notes for Chapter 7 (on the Riemann mapping theorem)
can be found here as a pdf
file.
Problem sheets
 Exercises 1 [Due Tuesday October 28th,
2003.]

Connectedness, CauchyRiemann equations, power series.
 Exercises 2 [Due Tuesday November 18th,
2003.]

Uniform convergence and its realation to complex integrals.
CasoratiWeierstrass theorem. Homotopy version of Cauchy's integral
formula for higher derivatives.
 Exercises 3 [Due Monday, January 5th
2004.]

Logs, simply connected, identity theorem, maximum modulus principle.
 Exercises 4 [Due Monday, February 2nd
2004.]

Residues, Laurent series, singularities.
 Exercises 5 [Due Monday, February 16th
2004.]

M(G) an algebra. Rouché's theorem.
 Exercises 6 [Due Monday, March 1st
2004.]

H(G) as a metric space. Local uniform convergence, differentiation map
continuous.
The exam paper set in
summer
1998,
summer
2000
summer
2002
are available in PDF format.
So are some
other years papers for this and other courses.
Updated March 30th, 2004
Richard M. Timoney