MATHEMATİCS III PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT209	MATHEMATİCS III	3	3	3	5

GENERAL INFORMATION
Language of Instruction :	Türkçe
Level of the Course Unit :	LİSANS, TYY: + 6.Düzey, EQF-LLL: 6.Düzey, QF-EHEA: 1.Düzey
Type of the Course :	Zorunlu
Mode of Delivery of the Course Unit	-
Coordinator of the Course Unit	Dr.Öğr.Üyesi PERİ GÜNEŞ
Instructor(s) of the Course Unit	Dr.Öğr.Üyesi TARIK ARABACI
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	Kompleks analiz özellikle analitik veya kompleks, türevli fonksiyonlar üzerinde çalışır. Bu ders, tek değişkenli kompleksanalitik fonksiyonların teorisini kavratmayı amaçlar. Temel aritmetik ve kompleks sayıların geometrisi ile başalnır ve CauchyRiemann denklemleri ve Cauchy integral formülü ile sürdürülür. Analitik fonksiyonların kuvvet seri gösterimleri ve temel rezidü teoremleri ile tamamlanır.
Contents of the Course Unit:	Bu dersde Kompleks sayıların temel konularını tartışacaktır. Temel fonksiyonlar; türev ve CauchyRiemann denklemleri; Cauchy integral teoremi; Morera teoremi; analitik fonksiyonların sıfırları; Maksimum ve minimum ilkesi; Cebrin temel teoremi; Laurent serileri; Tekil izole noktaların sınıflandırılması ; rezidü teoremi.

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
Türev ve Cauchy Riemann denklemlerini kullanabilir.
Doğrusal integraller ve Cauchy integral teoreminin uygulamalarını kavrayabilir.
Analitik fonksiyonlar için Cauchy’integral formulünü hesaplayabilir.
Laurent serilerini kullanabilir.
Rezidü teoremleri ile integral hesaplayabilir.
Rouché teoreminin uygulamalarını kavrayabilir.

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	-	Kompleks Sayılar üzerinde revizyon	-
2	-	Temel fonksiyonlar; sin z, cos z, sinh z, cosh z, exp(z).	-
3	-	Complex Fonksiyonların türevleri. Cauchy-Riemann denklemleri.	-
4	-	Doğrusal integraller, ilkel fonksiyonlar	-
5	-	Cauchy eşitsizliği. Liouville teoremi. Cebrin Temel Teoremi	-
6	-	Taylor Serileri	-
7	-	Kompleks analiz	-
8	-	ARA SINAV	-
9	-	Kompleks analiz	-
10	-	Analitik fonksiyonların sıfırları. Laurent serileri	-
11	-	Ayrık matematik	-
12	-	Ayrık matematik	-
13	-	Rezidü teoremi	-
14	-	Rezidü teoremi ile integral hesabı	-
15	-	Rouché teoremi.	-
16	-	FİNAL	-
17	-	FİNAL	-

SOURCE MATERIALS & RECOMMENDED READING

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Explains the fundamental engineering concepts of electrical and electronics science and relates them to the groundwork of electrical and electronics science.

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Uses theoretical and practical knowledge coming from electrical and electronics sciences, to find solutions to engineering problems.

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines the components and the underlying process of a system and designs an appropriate model related to electrical and electronics under reasonable constraints.
2	Designs a model related to electrical and electronics with modern techniques.

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines, detects and analyzes the areas of electrical and electronics engineering science applications and develops appropriate solutions.
2	Identifies, models and solveselectrical and electronics engineering problems by applying appropriate analytical methods.
3	Determines and uses the necessary electrical and electronics engineering technologies in an efficient way for engineering applications.

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess the responsibility and ability to design and conduct experiments for engineering problems by collecting, analyzing and interpreting data.
2	Possess the ability to conduct effective individual study.
3	Takes responsibility as a team work and contributes in an effective way.

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Monitors the developments in the field of electrical and electronics engineering technologies by means of books, internet and related journals and possess the required knowledge for the management, control, development and security of information technologies.
2	Develops positive attitude towards lifelong learning.

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Communicates effectively by oral and/or written form and uses at least one foreign language.
2	Possess sufficient consciousness about the issues of project management, practical applications and also environmental protection, worker's health and security.

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess professional and ethical responsibility and willingness to share it.
2	Possess sufficient consciousness about the universality of electrical and electronics engineering solutions and applications and be well aware of the importance of innovation.

WORKLOAD & ECTS CREDITS OF THE COURSE UNIT
Workload for Learning & Teaching Activities
Type of the Learning Activites	Learning Activities (# of week)	Duration (hours, h)	Workload (h)
Ders	14	3	42
Derse Ön Hazırlık ve Ders Sonrası Pekiştirme	14	3	42
Arazi Çalışması	0	0	0
Grup Çalışması / Ödevi	0	0	0
Laboratuvar	0	0	0
Okuma	1	2	2
Ödev	8	5	40
Proje Hazırlama	0	0	0
Seminer	0	0	0
Staj	0	0	0
Teknik Gezi	0	0	0
Web Tab. Öğrenme	0	0	0
Uygulama	0	0	0
Yerinde Uygulama	0	0	0
Mesleki Faaliyet	0	0	0
Sosyal Faaliyet	0	0	0
Tez Hazırlama	0	0	0
Alan Çalışması	0	0	0
Rapor Yazma	0	0	0
Final Sınavı	1	1	1
Final Sınavı Hazırlığı	0	0	0
Ara Sınav	1	1	1
Ara Sınav Hazırlığı	0	0	0
Kısa Sınav	0	0	0
Kısa Sınav Hazırlığı	0	0	0
TOPLAM	39	0	128