Syllabus ( MATH 671 )
|
Basic information
|
|
Course title: |
Operator Theory And Its Applications |
Course code: |
MATH 671 |
Lecturer: |
Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)
|
ECTS credits: |
7.5 |
GTU credits: |
3 (3+0+0) |
Year, Semester: |
1/2, Fall and Spring |
Level of course: |
Second Cycle (Master's) |
Type of course: |
Area Elective
|
Language of instruction: |
Turkish
|
Mode of delivery: |
Face to face
|
Pre- and co-requisites: |
MATH 350, MATH 502 |
Professional practice: |
No |
Purpose of the course: |
To teach spectral properties of some operator types and its applications by assuming to be known the fundamental concepts of Funtional Analysis |
|
|
|
Learning outcomes
|
|
Upon successful completion of this course, students will be able to:
-
Obtain the fundamental concepts and theorems of Operator Theory
Contribution to Program Outcomes
-
Define and manipulate advanced concepts of Mathematics
-
Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
-
Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
-
Written exam
-
Obtain spectral properties of some operators
Contribution to Program Outcomes
-
Define and manipulate advanced concepts of Mathematics
-
Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
-
Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
-
Written exam
-
Homework assignment
-
Determine the areas of applying of Operator Theory
Contribution to Program Outcomes
-
Define and manipulate advanced concepts of Mathematics
-
Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
-
Acquire scientific knowledge and work independently
Method of assessment
-
Written exam
-
Oral exam
-
Homework assignment
|
|
Contents
|
|
Week 1: |
Banach and Hilbert Spaces |
Week 2: |
Linear Functionals and Bounded Linear operators |
Week 3: |
Projection Operators and Unitary Operators |
Week 4: |
General Concepts and Propositions in Theory of Linear Operators |
Week 5: |
The Concept of Spectrum and Resolvent |
Week 6: |
The Graph of Operator |
Week 7: |
Spectral Analysis of Completely Continuous Operators |
Week 8: |
Midterm exam. Fredholm Theorems |
Week 9: |
Fixed point Theorems, Existance of Invariant Subspace for a Completely Continuous Operators |
Week 10: |
Spectral Analysis of Unitary Operators |
Week 11: |
Spectral Analysis of Self-Adjoint Operators |
Week 12: |
Completely Continuous Self-Adjoint Operators, Hilbert-Schmidt Theorem |
Week 13: |
Theory of Extension of Symmetric Operators |
Week 14: |
Examples on Differential Operators |
Week 15*: |
--- |
Week 16*: |
Final Exam |
Textbooks and materials: |
|
Recommended readings: |
Walter Rudin, Functional analysis, N. I. Akhiezer and I.M. Glazman, Theory of linear operators in Hilbert space L. A. Lusternik and V. J. Sobolev, Elements of Functional Analysis Erwin Kreyszig, Introductory functional analysis with applications |
|
* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
|
|
|
|
Assessment
|
|
|
Method of assessment |
Week number |
Weight (%) |
|
Mid-terms: |
8 |
40 |
Other in-term studies: |
|
0 |
Project: |
|
0 |
Homework: |
3, 5, 7, 9, 11, 13 |
10 |
Quiz: |
|
0 |
Final exam: |
16 |
50 |
|
Total weight: |
(%) |
|
|
|
Workload
|
|
|
Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
|
Courses (Face-to-face teaching): |
3 |
14 |
|
Own studies outside class: |
4 |
14 |
|
Practice, Recitation: |
0 |
0 |
|
Homework: |
7 |
6 |
|
Term project: |
0 |
0 |
|
Term project presentation: |
0 |
0 |
|
Quiz: |
0 |
0 |
|
Own study for mid-term exam: |
20 |
1 |
|
Mid-term: |
3 |
1 |
|
Personal studies for final exam: |
20 |
1 |
|
Final exam: |
3 |
1 |
|
|
|
Total workload: |
|
|
|
Total ECTS credits: |
* |
|
* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
|
|
|
-->