Syllabus Application
MATH 305
Complex Calculus
Faculty
Faculty of Engineering and Natural Sciences
Semester
Spring 2025-2026
Course
MATH 305 -
Complex Calculus
Time/Place
Time
Week Day
Place
Date
13:40-14:30
Mon
FASS-G018
Feb 16-May 22, 2026
13:40-15:30
Tue
FASS-G018
Feb 16-May 22, 2026
Level of course
Undergraduate
Course Credits
SU Credit:3, ECTS:6, Basic:6
Prerequisites
MATH 102
Corequisites
Course Type
Lecture
Instructor(s) Information
Gökalp Alpan
- Email: gokalp.alpan@sabanciuniv.edu
Course Information
Catalog Course Description
This course covers the field of complex numbers, functions of one complex variable; analytic functions, the Cauchy- Riemann equations, harmonic functions integration in the complex plane, Cauchy integral formula, power series, Laurent series and isolated singularities, theory of residues and applications, conformal mappings.
Course Learning Outcomes:
| 1. | Upon completion of this course, students should be able to: Operate with complex numbers; |
|---|---|
| 2. | Differentiate and integrate complex valued functions; |
| 3. | Distinguish analyticity from differentiability by real variables (Cauchy-Riemann equation); |
| 4. | Understand how analytic and harmonic functions are connected; |
| 5. | Formulate Cauchy Theorem and Cauchy Formula and apply them consciously for integration; |
| 6. | Identify Taylor and Laurent expansions and distinguish isolated singularities; |
| 7. | Apply Cauchy Residue Theorem to calculations of definite integrals; |
| 8. | |
| 9. | |
| 10. |
Course Objective
To give an introduction to main methods of Complex Analysis which are needed for successful activity in many fields (engineering, economics, etc.) and for developing of mathematical thinking, as well
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Course Materials
Resources:
(Textbook) Fundamentals of Complex Analysis, Applications to Engineering and Science (Third International
edition), E. B. Saff, A. D. Snider, 2003, Pearson. (We will cover a significant portion of Chapters 1-6.)
(Recommended) Complex Variables and Applications (Eighth Edition) James Ward Brown, Ruel
V.Churchill, 2008, McGraw Hill.
edition), E. B. Saff, A. D. Snider, 2003, Pearson. (We will cover a significant portion of Chapters 1-6.)
(Recommended) Complex Variables and Applications (Eighth Edition) James Ward Brown, Ruel
V.Churchill, 2008, McGraw Hill.