B.P. Rynne and M.A. Youngson, Linear Functional Analysis, Springer, 2008 (Chapters: 4, 6, 7, and 8)
Other Sources
1) Y. Eidelman, V. Milman, and A. Tsolomitis, Functional Analysis, AMS, GSM 66, 2004.
2) I. Gohberg and S. Goldberg, Basic Operator Theory, Birkhauser, 1981.
3) I. Gohberg, S. Goldberg, and M.A. Kaashoek, Basic Classes of Linear Operators, Birkhauser, 2004.
4) P.R. Halmos, A Hilbert Space Problem Book, Springer, 1982.
Course Schedules
Week
Contents
Learning Methods
1. Week
The adjoint of an operator
Oral presentation and applications
2. Week
Normal, self-adjoint and unitary operators
Oral presentation and applications
3. Week
The spectrum of an operator
Oral presentation and applications
4. Week
Positive operators and projections
Oral presentation and applications
5. Week
Compact operators
Oral presentation and applications
6. Week
Spectral theory of compact operators
Oral presentation and applications
7. Week
Self-adjoint compact operators
Oral presentation and applications
8. Week
The spectral theorem
Oral presentation and applications
9. Week
Midterm Exam Week
Midterm Exam
10. Week
Applications to integral and differential equations
Oral presentation and applications
11. Week
Fredholm integral equations
Oral presentation and applications
12. Week
Volterra integral equations
Oral presentation and applications
13. Week
Differential equations
Oral presentation and applications
14. Week
Eigenvalue problems and Green’s functions
Oral presentation and applications
15. Week
Final Exam Week
Final Exam
16. Week
Final Exam Week
Final Exam
17. Week
Final Exam Week
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Final Exam
1
60
Program Outcomes
PO-1
Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2
On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3
Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4
Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5
Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6
Use information and communication technologies with computer software in advanced level.
PO-7
Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8
Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10
Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Express the adjoint of an operator
LO-2
Express Normal, self-adjoint and unitary operators
LO-3
Express the spectrum of an operator and discuss its properties
LO-4
Understand positive operators and projections
LO-5
Express compact operators and discuss its properties
LO-6
Explain spectral theory of compact operators
LO-7
Discuss self-adjoint compact operators
LO-8
Explain the spectral theorem
LO-9
Apply operatos to integral and differential equations
LO-10
Understand Fredholm integral equations and apply them to operator theory
LO-11
Understand Volterra integral equations and apply them to operator theory
LO-12
Understand differential equations and apply them to operator theory
LO-13
Understand eigenvalue problems and Green’s functions and apply them to operator theory
