Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
FUNCTIONAL ANALYSIS II MAT 402 8 3 + 1 4 5
Ön Koşul Dersleri Functional analysis I should be taken.
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. METİN BAŞARIR Dersi Verenler Dersin Yardımcıları Research assitants of Mathematics Department Dersin Kategorisi Dersin Amacı To teach the notions of operator theory. To transform a given problem to an operator equation. To investigate existance, uniqueness and stability of the solution of an operator equation. Classification of operators. To analyse the solution methods. Dersin İçeriği Linear spaces. Dual spaces. Adjoint operators. Compact sets. Compact linear operator. Hilbert adjoint operators on Hilbert spaces. The notions of spectrum and resolvant.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - 1 - 4 - 15 - A - C - 2 - 1 - 4 - 15 - A - C - 3 - 1 - 4 - 15 - A - C - 4 - 1 - 4 - 15 - A - C - 5 - 1 - 4 - 15 - A - C - 6 - 1 - 4 - 15 - A - C - 7 - 1 - 4 - 15 - A - C - 8 - 1 - 4 - A - C - 9 - 1 - 4 - A - C - 10 - 1 - 4 - A - C - 11 - 1 - 4 - A - C - 12 - 1 - 4 - A - C - 13 - 1 - 4 - A - C - 14 - 1 - 4 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Basic concepts of linear operator theory
2 The space of bounded linear operators
3 Inverse operators
4 Dual spaces and adjoint operators
5 Hahn Banach theorem and its consequences
6 Dual space of a normed space
7 Adjoint, Hermitian, unitary and normal operators
8 Strong and weak convergence
9 Exam
10 Compact sets and compact linear operators
11 Compactness in normed spaces
12 Compactness criterion for some normed spaces
13 Compact linear operators
14 Hilbert adjoint operators in Hilbert spaces and their spectrum and resolvants

#### Kaynaklar

Ders Notu [1] Naylor, Arch; Linear Operator Theory in Engineering and Science, Springer-Verlag, 1982.
[2] Kreyszig, E.; Introductory Functional Analysis with Applications, John Wiley & Sons, 1989.
Ders Kaynakları

#### 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. X
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 40
KisaSinav 1 20
Odev 1 20
KisaSinav 2 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 4 64
Mid-terms 1 15 15
Quiz 2 10 20
Assignment 1 15 15
Toplam İş Yükü 162
Toplam İş Yükü /25(s) 6.48
Dersin AKTS Kredisi 6.48
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