21MAT316 COMPLEX ANALYSIS MATHEMATICS PAPER – VII-

Unit I-

Definition – Algebra of complex numbers – polar forms – regions – Limits – continuity – differentiability – CR equations – Analytic Functions – Harmonic Functions.

Unit II-

Conformal mappings – bilinear transformations – Special bilinear transformations – fixed points.

Unit III-

Introduction to complex Integration – Contour integral – Primitives – Cauchy-Goursat theorem – Winding number – Cauchy’s integral formula.

Unit IV-

Sequences – series – power series – uniform convergence of power series – Taylor’s series – Laurent’s series – Integration and differentiation of Power series.

Unit V-

Zeros and singularities of analytic functions – types of singularities – poles – residue theorem, Classification of Singularities – Residues – Poles and zeroes.

TEXTBOOKS:

1. H S Kasana, Complex variables and Theory and Applications, 2nd edition, Prentice Hall India.

REFERENCES:

1. S. Ponnusamy, Foundations of Complex Analysis, 2nd Edition, Narosa Publishing House, 2005.
2. J.W. Brown and R.V. Churchil, Complex Variable and Applications, 8th edition, McGraw Hill, 2008.
3. R. Roopkumar, Complex Analysis, 1st edition, Pearson Education, Chennai, 2014.