Functions of a complex variable. The complex derivative. Cauchy-Riemann equations. Holomorphic functions. Complex integration. The Cauchy-Goursat theorem. Cauchy's integral formula. Maximum module principle and applications. Power series. Analytical functions. Laurent series. Classification of singularities. Residue theorem and applications. Compliant transformations.
Basic Information
Mandatory:
-
Markushevich, Theory of Functions of a Complex Variable, AMS, 1970
-
Ahlfors, L. V., Complex Analysis, McGraw-Hill, 1979
-
Apostol, T. M., Mathematical Analysis, 1974
-
Conway, J. B., Functions of one complex Variable, Springer-Verlag, 1978
-
Rudin W, Real and Complex Analysis, McGraw-Hill, 1987
Complementary:
-
Markushevich, Theory of Functions of a Complex Variable, AMS, 1970
-
Ahlfors, L. V., Complex Analysis, McGraw-Hill, 1979
-
Apostol, T. M., Mathematical Analysis, 1974
-
Conway, J. B., Functions of one complex Variable, Springer-Verlag, 1978
-
Rudin W, Real and Complex Analysis, McGraw-Hill, 1987