Ders Planı

Lesson Information

Course Credit	3.0
Course ECTS Credit	5.0
Teaching Language of Instruction	İngilizce
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course	Compulsory
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	Z
Course Coordinator
Instructor (s)
Course Assistant	Assist. Prof. Dr. YUSUF ZEREN

Purpose and Content

The aim of the course	This course aims to investigate complex numbers, their notations and properties and introduction of the complex functions theory and give the complex sequences and series ,the conceptions of limit,continuity,complex differentation and entire functions and theorems related with these and applications.
Course Content	This course covers complex numbers and its basic properties ,topology of the complex plane ,sequence and series of complex numbers, complex valued functions and its basic properties , limit and continuity of the complex valued functions, complex differentationof the complex valued functions ,Cauchy-Riemann's equations , complex exponential ,complex power ,complex logarithmic and complex trigonometric functions , analytic and harmonic functions , integration of complex valued functions , Cauchy's integral theorem and Cauchy's integral ,the derivative of Cauchy formula and applications , Liouville's theorem ,Cauchy's inequality,esential theorem of algebra,Singularities, zeros and poles ,complex power series ,complex Taylor and Mac-Laurin series and Laurent series,classification of the singular points, residues,residue theorem and applications , conform tranformations .

The aim of the course

This course aims to investigate complex numbers, their notations and properties and introduction of the complex functions theory and give the complex sequences and series ,the conceptions of limit,continuity,complex differentation and entire functions and theorems related with these and applications.

Course Content

This course covers complex numbers and its basic properties ,topology of the complex plane ,sequence and series of complex numbers, complex valued functions and its basic properties , limit and continuity of the complex valued functions, complex differentationof the complex valued functions ,Cauchy-Riemann's equations , complex exponential ,complex power ,complex logarithmic and complex trigonometric functions , analytic and harmonic functions , integration of complex valued functions , Cauchy's integral theorem and Cauchy's integral ,the derivative of Cauchy formula and applications , Liouville's theorem ,Cauchy's inequality,esential theorem of algebra,Singularities, zeros and poles ,complex power series ,complex Taylor and Mac-Laurin series and Laurent series,classification of the singular points, residues,residue theorem and applications , conform tranformations .

Learning Outcomes

Have advanced theoretical and practical knowledge in mathematics and computer science.
Gain an in-depth knowledge on Computer Science including computer programming, word processing, database functions, accessing the internet and softwares.
Possess the knowledge of advanced research methods in mathematics-computer field.
Possess theoretical and practical knowledge in mathematics, computation and computer science.
Define computer programming, word processing, data functions, internete access and software programs.
Describe advanced research methods in the field of Mathematics-Computer Science.
Evaluate and interpret data using the knowledge and skills gained in the fields of mathematics and computer science.
Identify, define and analyze problems in the fields of mathematics and computer science; develop solutions based on research and evidence.
Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose.
Design and apply interactive experimental environments to get the definitions and first solutions of the problems of computer science and computer science and evaluate these environments.
Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account.
Perform all phases of life cycle in computer based systems.
Work effectively as an individual and as a team member to solve problems in the areas of mathematics and computer science.
Have the ability to act independently, use initiative and creativity.
Work effectively either individually or in multidisciplinary teams.
Evaluate advanced knowledge and skills in the field with a critical approach.
Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies.
Have the consciousness of the necessity of lifelong learning and continuously develop professional knowledge and skills.
Use the time effectively in the process of getting the conclusion with analytical thinking ability.
Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing.
Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation.
Have the awareness of professional and ethical responsibility and legal consequences of information applications
Use the knowledge about the field for the benefit to society.

Weekly Course Subjects

1	Complex numbers and its basic properties ,topology of the complex plane.
2	Sequence and series of complex numbers.
3	Complex valued functions and its basic properties.
4	Limit and continuity of the complex valued functions.
5	Complex derivative of the complex valued functions ,Cauchy-Riemann's equations.
6	Complex exponential ,complex power ,complex logarithmic and complex trigonometric functions.
7	Analytic and harmonic functions.
8	Integration of complex valued functions esential.
9	Cauchy's integral theorem and Cauchy's integra.Midterm Exam.
10	The derivative of Cauchy formula and applications.
11	Liouville's theorem ,Cauchy's inequality,essential theorem of algebra,Singularities, zeros and poles.
12	Complex power series ,complex Taylor and Mac-Laurin series and Laurent series,classification of the singular points.
13	Residues,residue theorem and applications.
14	Conform tranformations.

Resources

1. Başarır, M., Kompleks Değişkenli Fonksiyonlar Teorisi,Skarya akaitapevi,2002.
2.Başkan, T., Kompleks Fonksiyonlar Teorisi,Bursa,1998.
3. Mathews, J. W. & Howell, R. W., Complex Analysis,Jones and Barlett Publishers,Boston,2001.

CLASS 1

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CLASS 3

CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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