### MA2104 Complex Variables - [Only for 2024 batch onwards]

#### Course Details

**Analytic functions:**

Limits and continuity, differentiability and analyticity, analytic branches of inverse of functions, branches of logarithm, Cauchy-Riemann equations, harmonic conjugates.

**Complex integrals:**

Line integral, Cauchy's integral 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, elementary properties of the mapping of exponential, sine and cosine functions., Liouville's theorem, fundamental theorem of Algebra.Taylor and Laurent series.

**Residue Calculus:**

Singularities and their classification, Laurent series, residue theorem and argument principle, computing real integrals using residues.

#### Course References:

**Text:**

E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., John Willey & Sons, 2011. Ch. 13-16.

**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.