Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ADVANCED ANALYSIS II MAT 006 0 3 + 0 3 6
Ön Koşul Dersleri Advanced Analysis I
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü ZORUNLU Dersin Koordinatörü Prof.Dr. METİN BAŞARIR Dersi Verenler Prof.Dr. METİN BAŞARIR Dersin Yardımcıları Dersin Kategorisi Alanına Uygun Temel Öğretim Dersin Amacı The aim of this course is to give some concepts which are related to Phd level in Mathematics. Dersin İçeriği Lp spaces, Convergence types, Convergence in Lp spaces, Convergence in Measure spaces, Derivative and Anti-derivative ( Integral of monotone functions, The functions of bounded vibrations, The derivative of anti-derivative, Absolute continuity)
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Lp and L inifinite spaces knowing 1 - 2 - 4 - A - C - 2 - Convergence types knowing 1 - 2 - 4 - A - C - 3 - The relations of derivative and integral knowing 1 - 2 - 4 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Preliminaries
2 Lp spaces
3 Some inequalities
4 Riesz-Fischer theorem
5 L infinite space
6 The concept of convergence
7 Convergence in Lp
8 The convergence in measure spaces
9 Mid Exam
10 Differential and integral
11 Integral of monotone functions
12 The functions of bounded vibrations
13 The derivations of anti-derivative
14 Absolute continuity

#### Kaynaklar

Ders Notu
Ders Kaynakları

1- R.G.Bartle, The elements of real analysis, John Wiley and Sons, New York, 1964.

2- H.L.Royden, Real Analysis, MacMillan, New York, 1968.

3-P.R.Halmos, Measure Theory, Princeton, Springer, 1974.

4- S.K.Barberian, Measure and Integration, MacMillan, New York, 1965.

5- M.Balcı, Reel Analiz, Balcı Yayınları, , Ankara, 2000.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
2 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
3 Student completes the missing or limited knowledge by using the scientific methods. X
4 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
5 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
6 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
7 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
8 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
9 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
10 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
11 Student follows the necessary technological developments in his/her field, and s/he uses them. X
12 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 60
KisaSinav 1 20
Odev 1 20
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 20 20
Quiz 1 10 10
Assignment 1 4 4
Final examination 1 25 25
Toplam İş Yükü 155
Toplam İş Yükü /25(s) 6.2
Dersin AKTS Kredisi 6.2
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