Math 421 Fall 2002
maintained by Eyal Markman
1) Complex Numbers: algebraic and geometric properties, polar form,
powers and roots.
2) Analytic functions: Differentiability and Cauchy-Riemann equations,
Harmonic functions, examples.
3) Elementary functions of a complex variable: exponential and trigonometric
4) Path integrals: contour integration and Cauchy's integral formula;
Liouville's theorem, Maximum modulus theorem,
the Fundamental Theorem of Algebra.
5) Series: Taylor and Laurant expansions, convergence, term-by-term operations with infinite series.
6) Isolated singularities and residues. Essential singularities and poles.
Evaluation of Improper integrals via residues.
7) (If time permits)
Mappings by elementary functions and linear fractional transformations;