MATEMATİK III DERS TANITIM VE UYGULAMA BİLGİLERİ

Kodu	Dersin Adı	Yarıyıl	Süresi(T+U)	Kredisi	AKTS Kredisi
MAT209	MATEMATİK III	3	3	3	5

DERS BİLGİLERİ
Dersin Öğretim Dili :	Türkçe
Dersin Düzeyi	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Dersin Türü	Zorunlu
Dersin Veriliş Şekli	-
Dersin Koordinatörü	Assist.Prof. PERİ GÜNEŞ
Dersi Veren Öğretim Üyesi/Öğretim Görevlisi	Dr.Öğr.Üyesi TARIK ARABACI
Ders Ön Koşulu	Yok

AMAÇ VE İÇERİK
Amaç:	Complex analysis is the study of functions of a complex variable, in particular “analytic” or complex differentiable functions. This course develops some of the rich theory of complexanalytic functions of one variable, beginning with the basic arithmetic and geometry of complex numbers and proceeding to the CauchyRiemann equations and Cauchy’s integral formula. It continues with power series representation of analytic functions, the basic theory of residues, and possible further topics.
İçerik:	In this course basic concepts of complex numbers will be discussed. Elementary functions; Derivative and CauchyRiemann equations; Cauchy’s integral theorem; Morera’s theorem; Zeroes of analytic functions; Maximum and minimum principle; Fundamental theorem of algebra; Laurent series; Classification of singular isolated points; residue theorem.

DERSİN ÖĞRENME ÇIKTILARI (Öğrenciler, bu dersi başarı ile tamamladıklarında aşağıda belirtilen bilgi, beceri ve/veya yetkinlikleri gösterirler.)
The students will be able to use Derivative and Cauchy Riemann equations.
The students will be able to apply the Line integrals and the Cauchy’s integral theorem.
The students will be able to calculate Cauchy’s integral formula for analytic functions.
The students will be able to use Laurent series.
The students will be able to calculate integrals with the residue theorem.
The students will be able to apply Rouché’s theorem.

HAFTALIK DERS KONULARI VE ÖNGÖRÜLEN HAZIRLIK ÇALIŞMALARI
Hafta	Ön Hazırlık	Konular	Yöntem
1	-	Revisions on complex numbers.	-
2	-	Elementary functions sin z, cos z, sinh z, cosh z, exp(z).	-
3	-	Derivative of complex-valued functions. Cauchy-Riemann equalities.	-
4	-	Line integrals. Primitive function.	-
5	-	Cauchy’s integral theorem, Morera’s theorem.	-
6	-	Taylor series	-
7	-	Complex analysis	-
8	-	MID-TERM EXAM	-
9	-	Complex analysis	-
10	-	Zeros of analytic functions. Laurent Series.	-
11	-	Discrete math	-
12	-	Discrete math	-
13	-	Theory of Residues.	-
14	-	Computation of integrals with Residue Theorem.	-
15	-	Rouché’s theorem.	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

KAYNAKLAR

ÖLÇME VE DEĞERLENDİRME
Yarıyıl İçi Yapılan Çalışmaların Ölçme ve Değerlendirmesi	Etkinlik Sayısı	Katkı Yüzdesi	Açıklama

(0) Etkisiz	(1) En Düşük	(2) Düşük	(3) Orta	(4) İyi	(5) Çok İyi
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		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.

DERSİN İŞ YÜKÜ VE AKTS KREDİSİ
Öğrenme-Öğretme Etkinlikleri İş Yükü
Öğrenme-Öğretme Etkinlikleri	Etkinlik(hafta sayısı)	Süresi(saat sayısı)	Toplam İş Yükü
Lecture & In-Class Activities	14	3	42
Preliminary & Further Study	14	3	42
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	1	2	2
Assignment (Homework)	8	5	40
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	0	0	0
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	1	1
Preparation for the Final Exam	0	0	0
Mid-Term Exam	1	1	1
Preparation for the Mid-Term Exam	0	0	0
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	39	0	128