### MA2010 Complex Variables

#### Course Details

**Analytic functions:**

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.

**Residue Calculus:**

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.

#### Course References:

TEXT:

E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., John Willey & Sons, 2010.

REFERENCES:

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.