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

### 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, 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.

### Problem sheets

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.

### Past papers

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