MAT 527/528 : Functions of a Complex Variable I, II

A thorough introduction to functions of one complex variable for beginning graduate students. The first course includes complex numbers, analytic functions, the Cauchy-Riemann equations, power series, the maximum modulus principle, Cauchy's theorem, the calculus of residues, harmonic functions, and conformal mapping. The second semester includes analytic continuation, infinite products, elliptic functions, the gamma function, the Riemann mapping theorem, Picard's theorem, the Riemann Zeta function, and applications to physics and number theory. Prerequisite MAT 426 or permission.

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Last modified on Tuesday, January 12, 1999