| Course Name: | COMPLEX ANALYSIS II |
| Code | Course type | Regular Semester | Theoretical | Practical | Credits | ECTS |
| MATH 304 | 2 | 6 | 3 | - | 3 | 5 |
|
| Name of Lecturer(s)-Academic Title: | Jamal Gaderov - |
| Teaching Assistant: | - |
| Course Language: | English |
| Course Type: | Main |
| Office Hours | 8:45- 17:00
|
| Contact Email: | [email protected]
Tel:07507285243
|
| Teacher's academic profile: | MSc
|
| Course Objectives: | In this complex numbers an their graphical representations will be shown. Roots of unity has nice results they will be seen. Limit of complex valued functions, analytic and harmonic functions are given. Finally, Cauchy integral and its related topics will be discussed. |
| Course Description (Course overview): | Complex differentiation, Cauchy-Riemann equations, holomorphic functions, conformal mappings, contour integration, Cauchy's theorem, Taylor and Laurent series, open mapping theorem, maximum modulus principle, applications of the residue theorem. |
COURSE CONTENT| Week | Hour | Date | Topic | | 1 |
3 |
3-7/2/2019 |
Complex numbers and Graphical representations | | 2 |
3 |
10-14/2/2019 |
Complex numbers and Graphical representations |
| | 3 |
3 |
17-21/2/2019 |
Roots of unity and applications | | 4 |
3 |
24-28/2/2019 |
Roots of unity and applications |
| | 5 |
3 |
3-7/3/2019 |
Limit of complex valued functions. Continuity and some theorem | | 6 |
3 |
26-28/3/2019 |
Limit of complex valued functions. Continuity and some theorem |
| | 7 |
3 |
31/3-4/4/2019 |
Sequences in complex plane and their convergence | | 8 |
3 |
7-11/4/2019 |
Sequences in complex plane and their convergence |
| | 9 |
3 |
14-18/4/2019 |
Midterm Exam | | 10 |
3 |
21-25/4/2019 |
Analytic functions. Cauchy – Riemann equations |
| | 11 |
3 |
28/4-2/5/2019 |
Analytic functions. Cauchy – Riemann equations | | 12 |
3 |
5-9/5/2019 |
Complex integration. Cauchy’s theorem |
| | 13 |
3 |
12-16/5/2019 |
Complex integration. Cauchy’s theorem | | 14 |
3 |
19-23/5/2019 |
Cauchy integral and related topics |
| | 15 |
3 |
26-30/5/2019 |
Infinite series. Taylor and Laurent series | | 16 |
3 |
9-13/6/2019 |
Final Exam |
| | 17 |
3 |
16-20/6/2019 |
Final Exam |
|
COURSE/STUDENT LEARNING OUTCOMES | | | 1 | Basic tools of Complex analysis | | 2 | Analytic functions | | 3 | Complex integration |
|
COURSE'S CONTRIBUTION TO PROGRAM OUTCOMES
(Blank : no contribution, I: Introduction, P: Profecient, A: Advanced ) | Program Learning Outcomes |
Cont. | | 1 | Demonstrate an understanding of the common body of knowledge in mathematics. | P | | 2 | Demonstrates an understanding of pedagogical content knowledge, technology and perfectible assessment. | A | | 3 | Demonstrate the ability to think critically, research scientifically, and become modern and up-to-date. | I | | 4 | Understands the interrelationship of human development, cognition, and culture and their impact on learning. | | | 5 | Demonstrate the ability to apply analytical and theoretical skills to model and solve mathematical problems. | A | | 6 | Demonstrate the ability to effectively use a variety of teaching technologies and techniques and classroom strategies to positively influence student learning. | | | 7 | Understands how to form connections among educators, families, and the larger community to promote equity and access to education for his/her students. | | | 8 | Understands assessment and evaluation of student performance and learning and program effectiveness. | | | 9 | Communicates effectively and works collaboratively within the context of a global society. | |
|
| Prerequisites (Course Reading List and References): | Murray Spiegel , Complex Variables
Lecture notes |
| Student's obligation (Special Requirements): | Do projects, homework |
| Course Book/Textbook: | Complex Variables, Schaum Outline Murray Spiegel |
| Other Course Materials/References: | Lecture notes |
| Teaching Methods (Forms of Teaching): | Lectures, Excersises, Self Evaluation, Project |
COURSE EVALUATION CRITERIA
| Method | Quantity |
Percentage (%) | | Participation | 1 | 10 | | Quiz | 1 | 10 | | Homework | 1 | 10 | | Project | 1 | 10 | | Midterm Exam(s) | 1 | 20 | | Final Exam | 1 | 40 |
| Total | 100 |
Examinations: Essay Questions, Short Answers, Matching |
|
Extra Notes:
|
ECTS (ALLOCATED BASED ON STUDENT) WORKLOAD| Activities | Quantity | Duration (Hour) | Total Work Load | | Contact Hours (Theoretical hours + Practical hours/2) x Weeks | | | 0 | | Hours for off-the-classroom study | | | 0 | | Study hours for the Midterm Exam | | | 0 | | Study hours for the Final Exam | | | 0 | | Other | | | 0 | | ECTS | | | 0 | | | | 0 | | | | 0 | | Total Workload | 0 | | ECTS Credit (Total workload/25) | 0 |
|