# Complex Analysis (MATH346) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Complex Analysis MATH346 6. Semester 4 0 0 4 7
Pre-requisite Course(s)
Math 251
Course Language English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Team/Group. The course is designed to provide necessary backgrounds in Complex Analysis for students of Mathematics, 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, Classical Special Functions, Approximation Theory, Orthogonal Polynomials, Fourier Analysis, Filter Theory, System Theory, etc. The students who succeeded in this course; Perform the algebraic operations on complex numbers, understand conjugate of a complex number, represent a complex number in polar form. Understand the elementary functions defined on complex plane, understand the derivative, analyticity and harmonic functions. Recognize the simple and connected domains, understand the concept of integral and its applications on complex plane. Understand the series of complex numbers, residues, and apply residues to evaluate certain types of integrals. Understand the mappings on complex plane. Complex Nnumbers and elementary functions, analytic functions and integration, sequences, series and singularities of complex functions, residue calculus and applications of contour integration, conformal mappings and applications.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Complex Numbers and Their Properties, Elementary Functions, Limits, Continuity. pp. 1-53
2 Complex Differentiation, Applications to Ordinary Differential Equations. pp. 53-59
3 The Cauchy-Riemann Equations, Ideal Fluid Flow, Multi-valued Functions, The Notion of the Riemann Surface of an Analytic Function. pp. 60-85
4 Complex Integration, Cauchy’s Theorem, Cauchy’s Integral Formula. pp. 111-158
5 Applications of Cauchy’s Integral Formula, Liouville, Morera, Maximum-Modules Theorems. pp. 158-175
6 Mid-Term Examination
7 Complex Series, Taylor Series, Laurent Series. pp. 175-197
8 Singularities of Complex Functions, Infinite Products. pp. 221-247
9 Mittag-Leffler Expansions, Differential Equations on the Complex Plane. s. 158-195 (in other Refernces [1].)
10 Cauchy Residue Theorem, Evaluation of Definite Integrals, Principal Value Integrals. pp. 251-267
11 11. Week Integrals with Branch Points, the Argument Principal pp. 270-283
12 Rouche’s Theorem, Fourier and Laplace Transforms. pp. 284-298
13 Conformal Transformations, Critical Points and Inverse Mappings. pp. 343-360
14 Mapping Theorems. pp. 341-345 (in [1]) pp. 341-345 (in other References [1].)
15 Bilinear Transformations. pp. 299-313

### Sources

Course Book 1. Complex Variables and Applications, by J. W. Brown and R.V. Churchill, McGraw Hill, 2003. 2. Complex Variables: Introduction and Applications, by M.J. Ablowitz and A.S. Fokas, Cambridge Texts in Applied Mathematics. Cambridge University Press, 1997. 3. A Collection of Problems on Complex Analysis, by L.I. Volkovyski et al Dover Pub., 1991.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### 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 X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
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 X
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 X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
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 X
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) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
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. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 4 64
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 7 35
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 15 30
Prepration of Final Exams/Final Jury 1 25 25