Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
OPERATOR THEORY 801500715080 3 + 0 3.0 8.0

Prerequisites None

Language of Instruction Turkish
Course Level Graduate Degree
Course Type Compulsory
Mode of delivery Oral presentation, answer-question, discussion, solving problems
Course Coordinator
Instructors
Assistants
Goals Aims to investigate the self-adjoint operators and finds the spectrum and resolvent of these operators. Furthermore, kompact operators, uniter and normal operators, differential and product operators, pozitive and dissipative operators are studied.
Course Content Self adjoint operators, spectrum and resolvent, compact operators, Hilbert- Schmidt Theorem, Fredholm Theory, fixed point theorems, Uniter and normal operators, Uniter equivalence, diferential and product operators, Fourier transformations, positive and dissipative operators, Gato and Fresche derivatives
Learning Outcomes 1) Learns the self-adjoint operators and finds the spectrum and resolvent.
2) Studies the compact operators.
3) Learns the Hilbert-Schmidt Theorem and Fredholm Theory.
4) Learns the fix point theorems.
5) Studies uniter and normal operators, differential and product operators, positive and dissipative operators.

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Self adjoint operators Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
selfadjoint operators Lecture; Problem Solving; Discussion
Opinion Pool
Problem Based Learning 		Presentation (Including Preparation Time)
2. Week Spectrum and resolvent Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
3. Week Spectrum ve resolvent (continuation) Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
4. Week Compact operators Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
5. Week Hilbert- Schmidt Theorem Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
6. Week Fredholm Theory Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
7. Week Fixed point theorems Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
8. Week Uniter and normal operators Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
9. Week Uniter and normal operators (continuation) Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
10. Week Uniter equivalence Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
11. Week Differential and product operators Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
12. Week Fourier transformations Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
13. Week Positive and dissipative operators Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)
14. Week Gato and Fresche derivatives Lecture; Question Answer; Problem Solving; Discussion

 Presentation (Including Preparation Time)

Sources Used in This Course
Recommended Sources
Fonksiyonel Analizin Unsurları, L. A. Lusternik, V. J. Sobolev
Lineer Diferensiyel Operatörler, M. A. Naimark
Spektral Teoriye Giriş, B. M. Levitan

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 3
Work Hour outside Classroom (Preparation, strengthening) 14 1
Homework 3 10
Presentation (Including Preparation Time) 2 15
Midterm Exam 1 2
Time to prepare for Midterm Exam 1 55
Final Exam 1 2
Time to prepare for Final Exam 1 65
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
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Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • ECTS credits and course workload