MA2010 Complex Variables
Limits and continuity, differentiability and analyticity, analytic branches ofinverse of functions, branches of logarithm, Cauchy-Riemann equations, harmonic conjugates. Complex integral: Cauchy's theorem and integral formula, series of complex functions and the Weierstrass M-test, Taylor series, identity theorem, isolation of zeros of an analytic function, statements of open mapping, inverse function, Liouville?s theorem, fundamental theorem of Algebra.
Singularities and their classification, Laurent series, residue theorem and argument principle, computing real integrals using residues. Bilinear transformation: Bilinear transformation, conformal mapping, elementary properties of the mapping of exponential, sine and cosine functions.
E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., John Willey & Sons, 2010.
1. R.V Churchill & J.W. Brown: Complex Variables and Applications, Mc-Graw Hill, 1990.
2. S. Ponnusamy and H. Silverman, Complex Variables with Applications, Birkhauser, 2006.