| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Lınear Functıonal Analysıs II | MAT 502 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | LINEER FUNCTIONAL ANALYSIS-I |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. METİN BAŞARIR |
| Dersi Verenler | Prof.Dr. METİN BAŞARIR, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | The understanding of Banach algebras, Hilbert spaces, the dual spaces of Hilbert spaces, Dual operators, adjoint operators, simetric operators and self-adjoint operators, unitary operator, Cayley transformation, closed domain theorem |
| Dersin İçeriği | Banach algebras (algebra and Banach algebras, homomorphisms and isomorphisms, the spectrum and the Gelfand-Mazur Theorem), Hilbert spaces (Inner product and Hilbert spaces, orthonormal sets, the dual space of Hilbert space), Dual operators(adjoint operators, simetric operators and self-adjoint operators, unitary operator, Cayley transformation, closed domain) |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/ she recognizes the Banach algebras. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 2 | He/ she interprets Hilbert spaces. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 3 | He/ she recognizes Dual operators. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 4 | He/ she recognizes adjoint operators, simetric operators and self-adjoint operators, unitary operator. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 5 | He/ she interprets Cayley transformation and closed domain theorem. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 6 | He/ she interprets the fundamental theorems of Functional Analysis. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Algebra and Banach algebras | |
| 2 | Homomorphisms and isomorphisms, the spectrum | |
| 3 | Gelfand-Mazur Theorem | |
| 4 | Inner product and Hilbert spaces | |
| 5 | Orthonormal sets, the dual space of Hilbert space | |
| 6 | Dual operators | |
| 7 | Linear spaces, subspaces, convex sets, linear metric spaces | |
| 8 | Adjoint operators, simetric operators | |
| 9 | Mid-term | |
| 10 | Self-adjoint operators, unitary operator | |
| 11 | Cayley transformation | |
| 12 | Banach Steinhauss Theorem | |
| 13 | Hahn Banach extension theory | |
| 14 | Closed domain theory |
| 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. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 2 | 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 | |||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 7 | 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 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 | |||||
| 8 | 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 critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
| 9 | 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 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 | |||||
| 10 | 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 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 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 | |||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 60 |
| 1. Ödev | 10 |
| 1. Kısa Sınav | 20 |
| 2. Ödev | 10 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (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 (Saat) | 6,44 | ||
| Dersin AKTS Kredisi | 6 | ||