Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
DIVERGENCE SERIES MAT 506 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. METİN BAŞARIR Dersi Verenler Prof.Dr. METİN BAŞARIR Dersin Yardımcıları Dersin Kategorisi Dersin Amacı To apprehend the properties of infinite series and infinite products,series with random terms,absolute and conditional convergent series,Riemann Theorem,to understand the numerical calculation of series,product of infinite series,to learn the power series,complex sequences and series,Abel and Drichlet criteria,sequence of variable elements, discrete and uniform convergence. Dersin İçeriği Infinite series and infinite products(infinite series and convergence,series with positive elements,convergence criterias),The series with random elements(Leibnitz criteria),absolute and conditional convergent series,Riemann Theorem,the numerical calculation of series,product of infinite series,the power series(convergence domain and radius),complex sequences and series,Abel and Drichlet criteria,sequence of variable elements, discrete and uniform convergence,infinite products,Cauchy condition and absolute convergence,some attentions on divergence series,operations of limiting,operations C-,H-;operation of A-,operation of E-;
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she recognizes the properties of infinite series and infinite products. 1 - 2 - 3 - 14 - 15 - A - C - 2 - He/she distinguishes the series with random terms,absolute and conditional convergent series. 1 - 2 - 3 - 14 - 15 - A - C - 3 - He/she expresses the discrete and uniform convergence. 1 - 2 - 3 - 14 - 15 - A - C - 4 - He/she recognizes complex sequences and series . 1 - 2 - 3 - 14 - 15 - A - C - 5 - He/she expresses Abel and Drichlet criteria. 1 - 2 - 3 - 14 - 15 - A - C - 6 - He/she recognizes and interprets the sequence of variable elements. 1 - 2 - 3 - 14 - 15 - A - C - 7 - He)she calculates the series numerically. 1 - 2 - 3 - 14 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Infinite series and infinite products
2 Infinite series and convergence,series with positive elements,convergence criterias
3 The series with random elements
4 Leibnitz criteria,absolute and conditional convergent series
5 Riemann Theorem, the numerical calculation of series,
6 Product of infinite series
7 The power series,convergence domain and radius
8 Complex sequences and series, Abel and Drichlet criterias
9 intermediate examination
10 Sequence of variable elements, discrete and uniform convergence,
11 Infinite products,Cauchy condition and absolute convergence,
12 Some attentions on divergence series,operations of limitİNG
13 operations C-,H-;operation of A-,operation of E-;
14 operation of A-,operation of E-;

#### Kaynaklar

Ders Notu [1] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul
Ders Kaynakları [2] Maddox,I.J.; Elements of Functional Analysis, Cambridge Un.Press,1970,London.
[3] Şuhubi, Erdoğan; Fonksiyonel Analiz, İTÜ Vakfı, 2001, İstanbul
[4] Naylor, Arch; Linear Operator Theory in Engineering and Science, Springer-Verlag, 1982.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Student follows the current journals in his/her field and puts forward problems. X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
5 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
6 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
7 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
8 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
9 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
10 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
11 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
12 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
13 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
14 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
15 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
16 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
17 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level.
18 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
19 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
20 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 60
Odev 1 20
KisaSinav 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
Assignment 2 10 20
Final examination 1 25 25
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
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