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\begin{document}

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\centerline{\bf  Math 606 Syllabus Spring 2003}

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1. Power series, Taylor and Laurent expansions.
Weierstrass and Hurwitz theorems. Mittag-Leffler theorem on
$\Bbb C$. Infinite products. Entire functions and their
classification. Special functions.

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2. Conformal mapping. Normal families, Arzela's
theorem. The Riemann mapping theorem.
Schwarz-Christoffel transformations. Dirichlet Problem.

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3. Riemann surfaces. Basics; definition, holomorphic maps,
meromorphic functions, holomorphic and meromorphic
differentials, branch points,  Riemann-Hurwitz formula.

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4. Elliptic function theory.

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5. Illustration of applications of complex analysis in geometry,
isothermal coordinates, minimal surfaces, elasticity.


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