Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
LINEER FUNCTIONAL ANALYSIS I MAT 501 0 3 + 0 3 6
Ön Koşul Dersleri Funcional Analysis I-II
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. METİN BAŞARIR Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı Metric and Topological Spaces, Linear spaces and Linear metric spaces, The understanding of normed linear spaces, Convergence and completeness in these spaces, linear operators and functionals, Banach Steinhauss Theorem, Open mapping and Closed graph theorems, Hahn-Banach extension theorem,weak convergence Dersin İçeriği Metric and Topological Spaces (Metric and semi metric spaces, complete metric spaces, some concepts of metric and topological, continuous functions on metric and Topological Spaces,compact sets, category and uniform boundedness), Linear and linear metric spaces (Linear spaces, subspaces, dimensionality, factorspaces, convex spaces, linear metric spaces, paranorms ,seminorms and norms, basis, distributions), normed linear spaces (convergence and completeness, linear operators and functionals, Banach Steinhauss Theorem, Open mapping and Closed graph theorems, weak convergence)
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she distinguishes the difference between Metric and Topological Spaces. 1 - 2 - 3 - 9 - 14 - A - C - 2 - He/she describes Linear spaces and Linear metric spaces. 1 - 2 - 3 - 9 - 14 - A - C - 3 - He/she illustrates normed linear spaces. 1 - 2 - 3 - 9 - 14 - A - C - 4 - He/she explains the interpretation of linear operators and functionals. 1 - 2 - 3 - 9 - 14 - A - C - 5 - He/she expresses Banach Steinhauss Theorem, Open mapping and Closed graph theorem, Hahn-Banach extension theorems. 1 - 2 - 3 - 9 - 14 - A - C - 6 - He/she compares the concept of weak convergence and strong convergence. 1 - 2 - 3 - 9 - 14 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 9:Simulation 14:Self Study Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Basic concepts in metric and topological spaces
2 Metric and semi Metric spaces, complete metric spaces, some concepts of metric and topological
3 Continuous functions on Topological Spaces, compact sets
4 Category and uniform boundedness
5 Linear spaces, subspaces, dimensionality
6 Factor spaces, convex sets
7 Linear metric spaces
8 Paranorms ,seminorms and norms, basis, distributions
9 Mid-term
10 Normed linear spaces
11 Convergence and completeness
12 Banach Steinhauss Theorem, Open mapping and Closed graph theorems
13 Hahn-Banach extension theorem
14 Weak convergence

#### 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 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.
10 Student follows the current journals in his/her field and puts forward problems. X
11 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
12 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
13 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
14 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
15 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
16 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
17 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
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 50
Odev 1 20
Odev 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
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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