| Course Type | Elective Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 4 |
|---|
| Name of Lecturer(s) |
|
| Learning Outcomes |
At the end of this course, the students;
- Understand the definition of complex numbers and knows their properties.
- Define complex functions.
- Know functions of complex variables and can make applications related to these functions.
- Understand differentiability of complex functions.
- Know the concept of integral in complex functions.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | Calculus |
|---|
| Course Description | The course content includes the following topics: complex numbers, complex functions, complex sequence, limit and continuity in complex functions, exponential, logarithm, trigonometric, hyperbolic, inverse trigonometric functions, differentibility in complex functions, analytical functions, harmonic functions, integration of complex functions, Cauchy integral theorem and Cauchy derivative formula. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Complex numbers, geometric representations |
|
2nd Week |
Some elamanter complex functions, inverse trigonometric and inverse hyperbolic functions |
|
3rd Week |
Limit and continuity in complex functions |
|
4th Week |
Differentiability of complex functions |
|
5th Week |
Analytical functions, Cauchy-Rieman equations |
|
6th Week |
Determining analytic sets of functions |
|
7th Week |
Integral of complex functions, line integral |
|
8th Week |
Midterm |
|
9th Week |
Cauchy theorem and its applications, Cauchy integral formula and its results |
|
10th Week |
Harmonic functions |
|
11th Week |
Cauchy integral formula and applications |
|
12th Week |
Results of the Cauchy integral formula |
|
13th Week |
Complex number series |
|
14th Week |
Laurent's theorem and its applications |
|
15th Week |
General review |
|
| Recommended or Required Reading | Basic Complex Analysis - Jerrold E. Marsden
Complex Variables - Schoum's Outline Series - Murray R. Spigel |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Quiz |
2 |
10 |
| Total(%) |
|
50 |
| Contribution of In-term Studies to Overall Grade(%) |
|
50 |
| Contribution of Final Examination to Overall Grade(%) |
|
50 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
2 |
3 |
6 |
| Individual or group work |
13 |
2 |
26 |
| Preparation for Final exam |
1 |
24 |
24 |
| Course hours |
13 |
3 |
39 |
| Preparation for Midterm exam |
1 |
21 |
21 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
|
|
|
| Total Work Load | 120 |
| Total Work Load / 30 (h) | 4 |
| ECTS Credit of the Course | 4 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
