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Title Real and Complex Analysis (Code-09050601)

Real and Complex Analysis (Code-09050601)
SYLLABUS

S.No.

Topic

Domain

Hours as per UGC

1

  • Jacobians, Beta and Gama functions.
  • Double and Triple integrals.
  • Dirichlets integrals,
  • Change of order of integration in double integrals.

Must know

15

2

  • Fourier exceptional of piecewise monotonic functions.
  • Properties of Fourier Co-efficient,
  • Dirichlets conditions, Parseval’s identity for Fourier series.
  •  Fourier series for odd and even functions.
  • Half range series,change of intervals.

Must know

15

3

  • Extended Complex plane.
  • Stereographic projection of complex numbers.
  • Continuity and differentiability of complex functions.
  • Analytic functions, Cauchy –Riemann equations.
  • Harmonic functions.

Must know

15

4

  • Mapping by elementary functions,
  • Translation. Rotation, Magnification and Inversion.
  • Conformal mappings
  • Mobius transformations
  • Fixed points, Cross ratio, inverse Point and critical mappings

Nice to know

15

    Books Recommended;

  • T.M. Apostol: Mathematical Analysis, Narosa Publishing House, New Delhi, 1985
  • R.R. Goldberg : Real Analysis Oxford & IBH publishing Co., New Delhi, 1970
  • D. Somasundaram and B. Choudhary : A First Course in Mathematicl Analysis, Narosa Publishing

House, New Delhi, 1997

  • Shanti Narayan : A Course of Mathematical Analysis, S. Chand & Co., New Delhi.
  • R.V. Churchill & J. W. Brown: Complex Variables and Applications, 5th Ed., McGraw–Hill, New York, 1990.
  • Shanti Narayan : Theory of function of Complex Variable, S. Chand & co., New Delhi.
  • James Ward Brown and Ruel V. Churchill: Complex Variables and Applications, 8th Ed., McGraw– Hill, Hill International Edition,2009.
  • Joseph Bak and Donald j. Newman:  Complex Analysis,2nd Ed., Undergraduate Texts in Mathematics, Springer –Verlag, New York, Ine., New York 1997.