TRINITY COLLEGE DUBLIN

Complex Analysis for JS & SS Mathematics, SS Two-subject moderatorship

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, Cauchy-Riemann 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.

Exercises 1 [Due Tuesday October 28th, 2003.]: Connectedness, Cauchy-Riemann equations, power series.
Exercises 2 [Due Tuesday November 18th, 2003.]: Uniform convergence and its realation to complex integrals. Casorati-Weierstrass 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.

Updated March 30th, 2004
Richard M. Timoney