complexanalysis

MAT101 COMPLEX ANALYSIS

• Syllabus: Analytic functions as mappings, conformal mappings, Mobius transformations, branch of logarithm, Riemann Stieltjes integrals.

  • Power series representation of analytic functions, maximum modulus theorem, index of a closed curve,Cauchy’s theorem and integral formula on open subsets of C.

  • Homotopy, homotopic version of Cauchy’s theorem, simple connectedness, counting of zeros, open mapping theorem, Goursat’s theorem, Classification of singularities, Laurent series.

  • Residue, Contour integration, argument principle, Rouche’s theorem, Maximum principle, Schwarz’ lemma.

• Text: J B Conway, Functions of one complex variables, 2nd ed, Narosa Publishing House, New Delhi, 2002.

• Reference books.

  • [1] L.V. Ahlfors, Complex Analysis, Mc. Graw Hill Co., New York, 1988.

  • [2] T. W. Gamelin, Complex Analysis, Springer Verlag, 2008.

  • [3] L. Hahn, B. Epstein, Classical Complex Analysis, Jones and Bartlett, India, New Delhi, 2011.

  • [4] D. Ullrich, David Ullrich, Complex Made Simple, AMS, 2008

• Solution Manual by Andreas Kleefeld for Conway's book is here

• Lecture Hours: Tuesday to Friday, 10:50 - 11:45 @ Room -2 (Ground Floor/New Social Scienes Buiding)