Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Fıxed Poınt Theory and Its Applıcatıons I | MAT 625 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | |
Önerilen Seçmeli Dersler | 1. Topology 2. Functional Analysis |
Dersin Dili | Türkçe |
Dersin Seviyesi | Doktora |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Prof.Dr. MAHPEYKER ÖZTÜRK |
Dersi Verenler | Prof.Dr. MAHPEYKER ÖZTÜRK, |
Dersin Yardımcıları | |
Dersin Kategorisi | Alanına Uygun Temel Öğretim |
Dersin Amacı | To understand the concept of fixed point. |
Dersin İçeriği | Fixed Point, Contraction Mapping, single-valued and multivalued mappings in metric spaces, Banach Fixed Point Theorem, Extensions of Banach Fixed Point Theorem, Caristis Theorem and its Equivalents, Set valued Contractios, Generalized Contractions, Structure and Properties of the Fixed Point Sets,Picards Theorem, Iteration Methods, Cauchy Theorem, Applications of Banach Fixed Point Theorem to Reel Analysis, Linear Equation Systems, Differantial and Integral Equations. |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He\she comprehends different contraction mappings and understand the concept of fixed point | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
2 | He\she explains the single valued and multivalued maooings in metric spaces. | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
3 | He\she analysis the Banach fixed point theorem and some extensions of Banach fixed point theorem | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
4 | He\she explains the Caristi-Ekeland Theorem and its equivalence | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
5 | He\she explains the set-valued mappings and Generalized contraction mappings | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
6 | He\she comments the structure of fixed point sets and properties of these sets. | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
7 | He\she explains the Picard Theorem,iteration method and Cauchy Problem | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
8 | He\she explains the applications of Banach fixed point theorem to Linear Equation Systems, Differantial and Integral Equations | Lecture, Question-Answer, Problem Solving, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | The concept of fixed point, Different Contraction Mappings | |
2 | The single valued and multivalued mappings in metric spaces | |
3 | The Banach fixed point theorem | |
4 | The extensions of Banach fixed point theorem | |
5 | The Caristi-Ekeland Theorem and its equivalences | |
6 | Set valued mappings | |
7 | Genaralized Contraction mappings | |
8 | The structure and properties of fixed point sets | |
9 | Mid-term exam | |
10 | The Pickard´s theorem, iterations methods and Cauchy problem | |
11 | The applications of Banach fixed point theorem to real analysis | |
12 | The applications of Banach fixed point theorem to linear equation systems | |
13 | The applications of Banach fixed point theorem to Differantial Equations | |
14 | The applications of Banach fixed point theorem to Integral Equations |
Kaynaklar | |
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Ders Notu | |
Ders Kaynakları | 1. The Computation of Fixed Points and Its Applications,1976 |
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 | ||||||
1 | At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. | X | |||||
2 | Student completes the missing or limited knowledge by using the scientific methods. | X | |||||
3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | X | |||||
4 | Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. | X | |||||
5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | X | |||||
6 | At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. | X | |||||
7 | Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. | X | |||||
8 | Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. | X | |||||
9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | X | |||||
10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | X | |||||
11 | Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. | X |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 80 |
1. Ödev | 10 |
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 | 5 | 10 |
Final examination | 1 | 25 | 25 |
Performance Task (Seminar) | 1 | 10 | 10 |
Toplam İş Yükü | 161 | ||
Toplam İş Yükü / 25 (Saat) | 6,44 | ||
Dersin AKTS Kredisi | 6 |