Complex Analysis: Course Outline (MAT 407)
Course Contents
Algebra of complex numbers, Analytic functions, CR equations, Harmonic functions, Elementary functions, Branches of log z, Complex exponents, Contours, CauchyGoursat theorem, Cauchy integral formula, Morera’s theorem, Maximum moduli of functions, Liouville’s theorem, Fundamental theorem of algebra, Convergence of sequences and series, Taylor series, Laurent series, Power series, Residues and poles, Residues theorems, Zeros of analytic function, Zeros and poles, Evaluation of improper integrals, Integrals involving trigonometric functions, Integration around a branch point, Definite integrals involving sine and cosine, Argument principle, Rouche’s theorem, Inverse Laplace transform, Mapping of complex functions, Conformal mapping, Analytic continuation.
Text Books

Complex variables and applications byCall Number: 515.9 BROISBN: 9780071263283Publication Date: 2009
Other Books

by Brilleslyper, Michael
Dorff, Michael J.
McDougall, Jane M. 
by Krantz, Steven G.
Date Published: 2004
Pages: 238