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Title Real and Complex Analysis (Code 09010601)

S.N Unit Content Domain Hours as per UGC
1 One 1.       Jacobians, Beta and Gama functions.

2.       Double and Triple integrals.

3.       Dirichlets integrals,

4.       Change of order of integration in double integrals.

5.       Fourier expentionof piecewise monotonic functions.

6.       Properties of Fourier Co-efficient,

7.       Dirichlets conditions, Parseval’s identity for Fourier series.

8.        Fourier series for odd and even functions.

9.       Half range series,change of intervals.

Must Know 15
2 Two 1.       Extended Complex plane.

2.       Stereographic projection of complex numbers.

3.       Continuity and differentiability of complex functions.

4.       Analytic functions, Cauchy –Riemann equations.

5.       Harmonic functions.

Must know 15
3 Three 1.       Mapping by elementary functions,

2.       Translation. Rotation, Magnification and Inversion.

3.       Conformal mappings

4.       Mobius transformations

5.       Fixed points, Cross ratio, inverse Point and critical mappings

Must know


Nice to know


Books Recommended:

  • M. Apostol: Mathematical Analysis, Narosa Publishing House, New Delhi, 1985
  • R. Goldberg : Real Analysis Oxford & IBH publishing Co., New Delhi, 1970
  • 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.
  • 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.