| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT3008 | Complex Analysis | Spring | 3 | 0 | 3 | 4 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. SÜREYYA AKYÜZ |
| Course Objectives: | This course provides deep understanding of analytic or complex differentiable functions. The objective of this course is to cover complex analytic functions' theory. It starts with fundamental arithmetic and complex numbers geometry. Then it continues Cauchy-Riemann equations and Cauchy integral formula. The representation of functions with power series and basic residue theorems are given. |
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The students who have succeeded in this course; Students learn; o Derivative and how to use Cauchy-Riemann equations. o Line integrals and applications of Cauchy integral theorem. o Evaluating Cauchy’s integral formula for analytic functions. o How to use Laurent series. o Calculating integrals using Residue theorems. o Applications of Rouché theorem. |
| This course will discuss the basic concepts of complex numbers. Basic functions, the derivative and Cauchy-Riemann equations, Cauchy's integral theorem, Morera's theorem, zeros of analytic functions, maximum and minimum principle of the fundamental theorem of algebra; Laurent series; single classification of isolated points; residue theorem. |
| Week | Subject | Related Preparation | |
| 1) | Complex Numbers, Riemann Sphere, Sequences and Series. | ||
| 2) | Functions of Complex Variables, Limit, Continuity. | ||
| 3) | Derivative of Functions of Complex Variables, Cauchy-Riemann Conditions, Analytic Functions. | ||
| 4) | Modules of derivative and Geometric meaning of Argument,Concept of Conformal Mapping. | ||
| 5) | Linear Fractional Function and its Properties. | ||
| 6) | Mapping Properties of Some Fundamental Functions. | ||
| 7) | Integral of the Functions of Complex Variable and its Relation with Curve Integrals, Newton-Leibnitz Formula,Cauchy Integral Theorem. | ||
| 8) | Cauchys İntegral Formula, Cauchys İntegral Formula for Derivatives, Cauchy Type Integral. Midterm exam I | ||
| 9) | Sequences and Series of Analytic Functions, Weierstrass Theorem. Morera’s Theorem. | ||
| 10) | Power Series, Abel Theorem, Cauchy-Hadamard Formula, Cauchys Inequality, Liouville Theorem. | ||
| 11) | Uniqueness Theorem, Maximum Module Principle and Schwarz Lemma. | ||
| 12) | Laurent Series, Cauchy Formula for Coefficients. | ||
| 13) | Zeros of Analytic Functions and Orders of Zeros. | ||
| 14) | Disjoint Singular Points, Poles and Essential Singular Points, Riemann, Casoratti-Weierstrass and Picard Theorms. | ||
| Course Notes: | “Fundamentals of Complex Analysis with Applications to Engineering and Science (third edition)”, by E. B. Saff and A.D. Snider. Pearson Education, Inc. |
| References: | A.I. Markushevich “Theory of Functions of a Complex Variable”, “Complex variables and applications” Ruel V. Churchill, |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 16 | % 0 |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 5 | % 15 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 45 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 5 | 3 | 15 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 2 | 5 | 10 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 10 | 10 |
| Total Workload | 105 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |