Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
INTRODUCTION TO FIXED POINT THEORY MAT 471 7 2 + 0 2 5
Ön Koşul Dersleri Analysis I-II, Topology I-II
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MAHPEYKER ÖZTÜRK Dersi Verenler Doç.Dr. MAHPEYKER ÖZTÜRK Dersin Yardımcıları Dersin Kategorisi Dersin Amacı To learn fixed point theory as an interesting application of metric spaces, to understand th applications of this theory to numerical analysis, ordinary differential equations and integral equations and linear algebra. Dersin İçeriği Fixed Point, Types of Contraction Mappings, single-valued and multivalued mappings in metric spaces, Banach Fixed Point Theorem, Extensions of Banach Fixed Point Theorem, Caristi´s Theorem and its Equivalents, Picard´s Theorem and Iteration Methods, Cauchy Theorem, Applications of Banach Fixed Point Theorem to Reel Analysis, Linear Equation Systems, Differantial and Integral Equations.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He\she comprehends the types of contraction mappings and understands the concept of fixed point. 1 - 2 - 4 - 14 - 15 - A - C - 2 - He\she explains single-valued and multivalued mappings in metric spaces. 1 - 2 - 4 - 14 - 15 - A - C - 3 - He\she analysis the Banach fixed point theorem and extensions of Banach fixed point theorem. 1 - 2 - 4 - 14 - 15 - A - C - 4 - He\she explains Caristi-Ekeland theorem and its equivalents. 1 - 2 - 4 - 14 - 15 - A - C - 5 - He\she explains the Picard´s Theorem and Iteration Methods, Cauchy Theorem 1 - 2 - 4 - 14 - 15 - A - C - 6 - He\she realizes the applications of Banach fixed point theorem to real analysis, linear equation systems, differantial and integral equations. 1 - 2 - 4 - 14 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 The concept of fixed point and types of contraction mappings.
2 Single-valued mappings in metric spaces
3 Multi-valued mappings in metric spaces
4 Banach fixed point theorem
5 Extensions of Banach fixed point theorem
6 The Caristi-Ekeland theorem and its equivalents.
7 Generalized contraction mappings
8 Picard´s theorem and iteration methods.
9 Mid-term exams
10 Cauchy problem.
11 Application of Banach fixed point theorem to numerical analysis.
12 Application of Banach fixed point theorem to linear equation systems.
13 Application of Banach fixed point theorem to differential equations.
14 Application of Banach fixed point theorem to integral equations.

#### Kaynaklar

Ders Notu
Ders Kaynakları

[1] Topics in Metric Fixed Point Theory, 1990
[2] Handbook of Metric Fixed Point Theory,2001
[3] An Introduction to Metric Spaces and Fixed Point Theory, 2001
[4] Vasile Berinde, Iterative Approximation of Fixed Points, Springer, 2002

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language.
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 50
KisaSinav 1 15
Odev 1 20
KisaSinav 2 15
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 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 1 10 10
Quiz 2 10 20
Assignment 1 5 5
Final examination 1 10 10
Toplam İş Yükü 109
Toplam İş Yükü /25(s) 4.36
Dersin AKTS Kredisi 4.36
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