Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
* MAT 612 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. METİN BAŞARIR Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı The aim of this course is to give some concepts which are related to graduate level in Mathematics. Dersin İçeriği The elements of functions theory (Number fields, Topological prelinimanires, convergent sequnces and series, continuous functions) Differential Calculus (Differentiable and holomorf functions) Analiticity and Conformity, Convergence types in functions theory (pointwise convergence, regular convergence, local regular convergence and convergence into compact) Power series (analiticity) Cauchy theory, Laurent and Fourier series, Rezidü Calculus
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - 1 - 2 - 3 - 14 - A - C - 2 - 1 - 2 - 3 - 14 - A - C - 3 - 1 - 2 - 3 - 14 - A - C - 4 - 1 - 2 - 3 - 14 - A - C - 5 - 1 - 2 - 3 - 14 - A - C - 6 - 1 - 2 - 3 - 14 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 14:Self Study Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 The elements of function theory
2 Convergent sequences and series
3 Differential calculus
4 Analiticity and conformity
5 Convergence types in funcitons theory
6 Power series
7 Cauchy theory
8 Cauchy integral theory
9 Laurent and taylor series
10 Mid exam
11 Rezidues Calculus
12 Cauchy-Riemann-Weierstrass in functions theory
13 Open mapping theorem and maksimum principle
14 General Review

#### Kaynaklar

Ders Notu

-Theory of Compleks Functions, R. Remmert, Springer-Verlag, London, New York, 1991.
-Modern analysis and topology, N.R. Howes, Springer-Verlag, New York, 1995.

Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 80
Odev 1 10
Odev 2 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 15 15
Assignment 2 15 30
Final examination 1 18 18
Toplam İş Yükü 159
Toplam İş Yükü /25(s) 6.36
Dersin AKTS Kredisi 6.36
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