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MATH 466

Complex Analysis II

3 credits · Undergraduate

Fall 2022

Topics

  • Holomorphic functions and Cauchy’s theorem
  • Open mapping and maximum modulus principles
  • Meromorphic functions, Laurent series and residues
  • Argument principle
  • Riemann mapping theorem and analytic continuation
  • Riemann surfaces
  • Periodic meromorphic functions on tori
  • Weierstrass and Jacobi elliptic functions
  • Time permitting: higher-genus algebraic curves, holomorphic differentials, Abel’s theorem, theta functions and Jacobi inversion

Readings

  • L. V. Ahlfors. Complex Analysis (supplementary).
    Recommended / optional / reference
  • H. M. Farkas and I. Kra. Riemann Surfaces, 2nd edition. Springer, 1992 (supplementary).
    Recommended / optional / reference
  • Elias M. Stein and Rami Shakarchi. Complex Analysis. Princeton University Press, 2003.
    Listed reading
Sources