| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Functıonal Analysıs and Its Applıcatıons | MAT 548 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. MUSTAFA ERÖZ |
| Dersi Verenler | Prof.Dr. MUSTAFA ERÖZ, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | The importance of tecniques of functional analysis in the fields of applied mathematics and engineering is gettting The aim of this course is to learn these tecniques which are powerful tools in problem solving and use them efficiently. |
| Dersin İçeriği | Metric spaces, Banach and Hilbert spaces,Fundamental theorems for normed spaces,Banach fixed point theorem,Contraction mapping principle in metric spaces,Some applications of contraction mapping pr. Application of fixed point theorem to linear equations, Application of fixed point theorem to linear equations,Application of fixed point theorem to integral equations, Differentiation of nonlinear operators, Gateaux derivative, Frechet derivative, Newton method for nonlinear operator equations, Application of Newton method to nonlinear algebraic equations, Application of Newton method to integral equations. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Students will have explained Banach fixed point theorem. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| 2 | Students will have applied fixed point theorem to linear equations. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| 3 | Students will have applied fixed point theorem to differential equations. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| 4 | Students will have applied fixed point theorem to integral equations. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| 5 | Students will have defined Gateaux and Frechet derivatives of nonlinear operators. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| 6 | Students will have explained how to use Newton method in solving nonlinear operator equations. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Metric spaces, Banach and Hilbert spaces | |
| 2 | Fundamental theorems for normed spaces | |
| 3 | Banach fixed point theorem | |
| 4 | Contraction mapping principle in metric spaces | |
| 5 | Some applications of contraction mapping pr. | |
| 6 | Application of fixed point theorem to linear equations | |
| 7 | Application of fixed point theorem to linear equations | |
| 8 | Application of fixed point theorem to integral equations | |
| 9 | Differentiation of nonlinear operators | |
| 10 | Gateaux derivative | |
| 11 | Frechet derivative | |
| 12 | Newton method for nonlinear operator equations | |
| 13 | Application of Newton method to nonlinear algebraic equations | |
| 14 | Application of Newton method to integral equations |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
| 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 | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | ||||||
| 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. | ||||||
| 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. | ||||||
| 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. | ||||||
| 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. | ||||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 50 |
| 1. Ödev | 50 |
| 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 | 1 | 10 | 10 |
| Final examination | 1 | 20 | 20 |
| Toplam İş Yükü | 146 | ||
| Toplam İş Yükü / 25 (Saat) | 5,84 | ||
| Dersin AKTS Kredisi | 6 | ||