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MATH 505
Complex Analysis

Faculty Faculty of Engineering and Natural Sciences
Semester Fall 2025-2026
Course MATH 505 - Complex Analysis
Time/Place
Time
Week Day
Place
Date
14:40-16:30
Wed
FASS-1103
Sep 29, 2025-Jan 3, 2026
12:40-13:30
Thu
FENS-G025
Sep 29, 2025-Jan 3, 2026
Level of course Masters
Course Credits SU Credit:3, ECTS:10
Prerequisites -
Corequisites -
Course Type Lecture

Instructor(s) Information

Nihat Gökhan Göğüş

Course Information

Catalog Course Description
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.
Course Learning Outcomes:
1. Comprehend the basic theory of analytic functions of a complex variable.
2. Be able to pursue a study of Riemann Surfaces.
3. Be able to apply ideas from complex analysis to different branches of mathematics.
4. Be prepared to take the complex analysis qualifying examination.
Course Objective
The course covers the material listed below. Chapters refer to the above mentioned textbook.

• Chapters 1: Complex numbers

• Chapter 2: Complex differentiation

• Chapter 3: Linear fractional transformations

• Chapter 4: Elementary functions

• Chapter 5: Power series

• Chapter 6: Complex integration

• Chapter 7: Simple versions of Cauchy's theorem and consequences

• Chapter 8: Laurent series and isolated singularities

• Chapter 9: Cauchy's theorem

• Chapter 10: Further development of basic complex function theory.
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Course Materials

Resources:
Technology Requirements:

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