MA 5360 Complex Analysis Course
contents: Unit I: Topology
of the complex plane, Riemann sphere, limits, continuity and
differentiability, Analytic functions, harmonic functions and multi-valued
functions.
Unit II: Convergence
of numerical series, Radius of convergence of power series, and power series
as an analytic function, Laurent series.
Unit III: Cauchy's
integral theorem, Cauchy integral formula, Morera's theorem, Taylor`s
theorem, Laurent's theorem, Liouville's theorem, Schwarz lemma; Maximum
Modulus Principle. Unit IV: Conformal mappings, linear
fractional transformations, Classification of singularities, Cauchy's residue
theory and evaluation of real integrals.
Text Books: 1.
S. Ponnusamy and H. Silverman: Complex Variables with
Applications, Birkhauser, Boston, 2006. 2.
J.B. Conway: Functions of one Complex Variables, 2nd edition,
Springer-Verlag, 1978. Reference: 1.
S. Ponnusamy: Foundations of Complex
Analysis, Second Edition, Narosa Publishing House, 2005 2.
L. Ahlfors: Complex Analysis,
2nd ed., McGraw-Hill, New York, 1966. 3.
J.W. Brown and R.V. Churchil,
Complex Variables and Applications, McGraw Hill, 2008 4.
T.W. Gamelin: Complex Analysis, Springer-Verlag,
2001. |