ECTS - Complex Variables and Applications
Complex Variables and Applications (MATH274) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Complex Variables and Applications | MATH274 | Diğer Bölümlere Verilen Ders | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH 152 or MATH 158 |
| Course Language | English |
|---|---|
| Course Type | Service Courses Given to Other Departments |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The course is designed to provide necessary backgrounds in Complex Analysis for students of Engineering and Physical Sciences. The topics covered by this course have numerous applications in Differential Equations, Inverse Scattering Problems, Matrix Theory, Operator Theory, Probability Theory, Elliptic Functions, Approximation Theory, Orthogonal Polynomials, Fourier Analysis, Filter Theory, System Theory, etc. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Complex Numbers and Functions. Analytic Functions. Elementary Functions. Line Integral and Cauchy Theorem. Power, Taylor, Maclaurin Series and Laurent series. Residues and Poles. Conformal Mapping. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Sums and Products, Basic Algebraic Properties, Moduli, Complex Conjugates, Exponential Forms, Products, Quotients in Exponential Form, Roots of Complex Numbers. | pp. 1-28 |
| 2 | Functions of a Complex Variable, Limits, Continuity, Derivatives, Differentiation Formulas, Cauchy-Riemann Equations, Analytic Functions, Harmonic Functions, | pp. 33-78 |
| 3 | The Exponential Function, The Logarithmic Function, Complex Exponents, Trigonometric Functions, Hyperbolic Functions | pp. 87-105 |
| 4 | Contours, Contour Integrals, Antiderivatives, Cauchy- Goursat Theorem. | pp. 111-148 |
| 5 | Simple and Multiple Connected Domains, Cauchy Integral Formula, Liouville’s Theorem, Maximum Modulus Principle | pp. 149-171 |
| 6 | Convergence of Series, Taylor Series, Laurent Series, Absolute and Uniform Convergence, Continuity of Sums and Power Series. | pp. 178-204 |
| 7 | Midterm | |
| 8 | Integration and Differentiation of Power Series, Uniqueness of Series Representation | pp. 206-215 |
| 9 | Residues, Cauchy’s Residue Theorem, Using a Single Residue, Isolated Singular Points, Residues at Poles. | pp. 221-236 |
| 10 | Zeros of Analytic Functions, Zeros and Poles, Behaviour of Functions Near Isolated Singular Points. | pp. 239-250 |
| 11 | Evaluation of Improper Integrals, Improper Integrals from Fourier Analysis, Jordan’s Lemma. | pp. 251-265 |
| 12 | Evaluation of Improper Integrals, Improper Integrals from Fourier Analysis, Jordan’s Lemma. | pp. 251-265 |
| 13 | Linear Transformations, The transformation w=1/z , Linear Fractional Transformations, An Implicit Form. | pp. 299-311 |
| 14 | The Transformation w=sin(z) , Mappings by z^2 , Branches of z^(1/2) , Square Roots of Polynomials. | pp. 318-334 |
| 15 | Preservation of Angles, Transformations of Harmonic Functions, Transformations of Boundary Condition | pp. 343-358 |
Sources
| Course Book | 1. Complex Variables and Applications, by J. W. Brown and R.V. Churcill, McGraw Hill, 2003 |
|---|---|
| Other Sources | 2. Fundamentals of Complex Analysis with applications to Engineering and Science 3th Edition,by E.B. Saff and A. D. Snider, Pearson Hall, 2003. |
| 3. A Collection of Problems on Complex Analysis, by L.I. Volkovyski et al Dover Pub., 1991 | |
| 4. Complex Variables: Introduction and Applications, by M.J. Ablowitz and A.S. Fokas, Cambridge Texts in Applied Mathematics. Cambridge University Press, 1997. | |
| 5. An Introduction to Complex Analysis: Classical and Modern Approaches, by W. Tutschke, H. L. Vasudeva, Chapman & Hall / CRC, 2005 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area | |||||
| 2 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research | |||||
| 3 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary | |||||
| 4 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study | |||||
| 5 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework | |||||
| 6 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility | |||||
| 7 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation | |||||
| 8 | To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) | |||||
| 9 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge | |||||
| 10 | Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. | |||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 7 | 4 | 28 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 15 | 30 |
| Prepration of Final Exams/Final Jury | 1 | 18 | 18 |
| Total Workload | 132 | ||