Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
CONTINUED FRACTIONS WITH APLICATIONS MAT 558 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Dr.Öğr.Üyesi BAHAR DEMİRTÜRK BİTİM Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Alanına Uygun Temel Öğretim Dersin Amacı To generalize subjects and methods of approximations theory and rational approximation of numbers Dersin İçeriği The methods of approximation theory and rational approximation of numbers
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she knows basic knowledge related with continued fractions. 1 - 4 - 15 - A - C - 2 - He/she compares the continued fractions and the power series. 1 - 4 - 15 - A - C - 3 - He/she finds the convergence of continued fractions. 1 - 4 - 15 - A - C - 4 - He/she computes continued fractions of Fibonacci numbers. 1 - 4 - 15 - A - C - 5 - He/she computes the periodic continued fractions 1 - 4 - 15 - A - C - 6 - He/she solves the numeric problems. 1 - 4 - 15 - A - C - 7 - He/she computes example of this fractions. 1 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Definitions and basic concepts
2 Formal definitions and notations.
3 Some particular examples.
4 From pover series to continued fractions.
5 From continued fractions to pover series.
6 Classical convergence theorems.
7 Worpitzkys theorem.
8 Classical remark on convergence.
9 Exam
10 Another concept of convergence.
11 Modified approximants.
12 Computation of approximants
13 Tail sequences, some properties of linear fractional transformations.
14 Speed of convergence, general convergence.

#### Kaynaklar

Ders Notu

Rational Approximations and Orthogonality, E.M. Nikishin and V.N. Sorakin

Ders Kaynakları

Continued Fractions with Applications,L. Lorentzen and H. Waadeland, 1992.

#### 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 understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 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
7 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
8 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
9 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
10 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 10
PerformansGoreviSeminer 2 30
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 0 0 0
Assignment 1 20 20
Performance Task (Seminar) 0 0 0
Final examination 1 20 20
Toplam İş Yükü 156
Toplam İş Yükü /25(s) 6.24
Dersin AKTS Kredisi 6.24
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