THIS COURSE WILL BE OFFERED AS A TUTORIAL.
The calculus of complex-valued functions turns out to have unexpected simplicity
and power. As an example of simplicity, every complex-differentiable function
is automatically infinitely differentiable. As examples of power, the so-called
"residue calculus" permits the computation of "impossible" integrals, and "conformal
mapping" reduces physical problems on very general domains to problems on the
round disc. The easiest proof of the Fundamental Theorem of Algebra, not to
mention the first proof of the Prime Number Theorem, used complex analysis.
Evaluation will be based primarily on classwork, homework, and exams. Prerequisite:
Mathematics 301 or 305.