COMPLEX ANALYSIS
Complex Plane, connected and compact sets. Extended complex plane: Stereographic projection. Complex valued functions, Analytic functions, C-R equation, Harmonic functions. Construction of an analytic functions.
Complex Integration, Complex line Integrals, Cauchy’s integral theorem, Cauchy’s Fundamental theorem, Indefinite integrals, fundamental theorem of Integral Calculus for complex functions.
Cauchy’s Integral Formula, Analyticity of the derivative of an analytic function, Liouville’s theorem, Poisson’s Integral formula, Morera’s theorem, Maximum modulus principle. Taylor’s and Laurent’s Series
Singularities. Meromorphic functions and Entire functions. Riemann’s theorem, Casorati-Weirstrass theorem. Rouche’s theorem. Fundamental theorem of algebra. Cauchy’s Residue theorem.
Contour integration. Conformal mapping (Introduction).Bilinear transformation and their simple properties . Powerseries.
- Complex Analysis , Purohit and Goyal , Jaipur Publishing House,2015
- Complex Variables: Theory and Applications ,H.S.Kasana, Prentice Hall, Delhi,2005
- Introduction to Complex Analysis, S.Ponnuswamy, Narosa Publishers,2011
- Theory and Problems of Complex Variables, R.Murray Spiegel , Schaum Outline Series,1974
- Complex Variables and Application, Brown and Churchill, McGraw Hills Book Co.,2010.
