MATH 3CF3 - Theory of Complex Functions

3 unit(s)

Definitions, proofs, and the geometry of complex functions. Complex numbers, polar representation, stereographic projection and the point at infinity. Complex functions, powers, roots, exponential, logarithm and their mapping properties, analytic functions, conformal mappings, fractional linear transformations. Integrals, contours, independence of path, harmonic conjugates, maximum principle, Cauchy and Morera Theorems, Cauchy Integral Formula. Series, power series, manipulations of series, analytic continuation, isolated singularities, Laurent series. Residues, integrals of rational functions, branch points, improper integrals. Logarithmic integrals, argument principle, Rouch Theorem, winding numbers.
Three lectures, one tutorial; one term
Prerequisite(s): MATH 1C03 and 2XB3 (or MATH 2XX3); or permission of the instructor
Not open to students with credit in MATH 3X03 .