Course Name Code Semester T+U Hours Credit ECTS
Linear Functional Analysis II MAT 502 0 3 + 0 3 6
Precondition Courses LINEER FUNCTIONAL ANALYSIS-I
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. METİN BAŞARIR
Course Lecturers Prof.Dr. METİN BAŞARIR,
Course Assistants
Course Category
Course Objective 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
Course Content 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)
# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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
Resources
Course Notes [1] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul
Course Resources [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.
Order Program Outcomes Level of Contribution
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
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Ödev 10
1. Kısa Sınav 20
2. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6