Complex Analysis (MATH 505)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Nihat Gökhan Göğüş -nggogus@sabanciuniv.edu,
English
Doctoral, Master
--
Formal lecture
Interactive,Communicative,Discussion based learning
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CONTENT

Analytic functions, Cauchy Riemann equations, conformal mappings. Cauchy integral formula. Power series and Laurent expansion. Residue theorem and its applications. Infinite products and Weierstarss theorem. Global properties of analytic functions, analytic continuation.

OBJECTIVE

Refer to the course content and learning outcomes.

LEARNING OUTCOME

Comprehend the basic theory of analytic functions of a complex variable.
Be able to pursue a study of Riemann Surfaces.
Be able to apply ideas from complex analysis to different branches of mathematics.
Be prepared to take the complex analysis qualifying examination.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 60
Midterm 40

RECOMENDED or REQUIRED READINGS

Readings

John B. Conway, Functions of One Complex Variable, Springer-Verlag, 1978.
Lars V. Ahlfors, Complex Analysis, McGraw-Hill, 1966.
Raghavan Narasimhan, Complex Analysis in One Variable, Birkhauser, 1985.
Forster, Otto, Lectures on Riemann surfaces , Graduate texts in mathematics; 81 Springer-Verlag New York Inc.1981