Syllabus Application
Complex Analysis
MATH 505
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Complex Analysis - MATH 505
Classroom:
FASS-1103,FENS-G025
Level of course:
Masters
Course Credits:
SU Credit:3.000, ECTS:10
Prerequisites:
-
Corequisites:
-
Course Type:
Lecture
Instructor(s) Information
Nihat Gökhan Göğüş
- Email: nggogus@sabanciuniv.edu
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.