Calculus in one Complex Variable

Basic information

Workload: 

60 hours

Prerequisite: 

Calculus in several Variables, Real Analysis 

Syllabus: 

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.

 

Teaching Plan

Bibliography

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