| Course Name: | FUNCTIONAL ANALYSIS II |
| Code | Course type | Regular Semester | Theoretical | Practical | Credits | ECTS |
| MATH 404 | 2 | 8 | 3 | - | 3 | 5 |
|
| Name of Lecturer(s)-Academic Title: | Orhan Tuğ - MSc |
| Teaching Assistant: | - |
| Course Language: | English |
| Course Type: | Non-area Elective |
| Office Hours | 14:30-16:30, Tuesday
|
| Contact Email: | [email protected]
Tel:07501644439
|
| Teacher's academic profile: | Asst Lecturer
|
| Course Objectives: | This course aims to contribute really high level functional analysis that is used in the applied mathematics only. But the course satisfy the main topological structure on operator theory both in Banach space and inner product space. |
| Course Description (Course overview): | Hahn-Banach theorem; open mapping theorem; uniform boundedness theorem, Krein-Milman theorem. Applications, convergent and divergent sequences, series, Matrix Transformation in sequence spaces |
COURSE CONTENT| Week | Hour | Date | Topic | | 1 |
3 |
3-7/2/2019 |
Introduction to Linear operators | | 2 |
3 |
10-14/2/2019 |
Bounded and Continuous linear operators I |
| | 3 |
3 |
17-21/2/2019 |
Bounded and Continuous linear operators II | | 4 |
3 |
24-28/2/2019 |
Linear functionals |
| | 5 |
3 |
3-7/3/2019 |
Dual Spaces | | 6 |
3 |
26-28/3/2019 |
Application of duality on sequence spaces |
| | 7 |
3 |
31/3-4/4/2019 |
Hilbert Space | | 8 |
3 |
7-11/4/2019 |
Midterm Exam |
| | 9 |
3 |
14-18/4/2019 |
Midterm Exam | | 10 |
3 |
21-25/4/2019 |
Orthogonal complements and direct sums |
| | 11 |
3 |
28/4-2/5/2019 |
Orthonormal sets and sequences I | | 12 |
3 |
5-9/5/2019 |
Orthonormal sets and sequences II |
| | 13 |
3 |
12-16/5/2019 |
Series related to Orthonormal sets and sequences | | 14 |
3 |
19-23/5/2019 |
Hilbert-Compact operators |
| | 15 |
3 |
26-30/5/2019 |
Self-Adjoint, Unitary and Normal Operators | | 16 |
3 |
9-13/6/2019 |
Final Exam |
| | 17 |
3 |
16-20/6/2019 |
Final Exam |
|
COURSE/STUDENT LEARNING OUTCOMES | | | 1 | student will be able to realize understanding of linear operators and operator theory | | 2 | student will be able to realize understanding of inner product space orthogonal structure | | 3 | student will be able to realize Understanding the application of inner products |
|
COURSE'S CONTRIBUTION TO PROGRAM OUTCOMES
(Blank : no contribution, I: Introduction, P: Profecient, A: Advanced ) | Program Learning Outcomes |
Cont. | | 1 | Demonstrate an understanding of the common body of knowledge in mathematics. | I | | 2 | Demonstrates an understanding of pedagogical content knowledge, technology and perfectible assessment. | I | | 3 | Demonstrate the ability to think critically, research scientifically, and become modern and up-to-date. | P | | 4 | Understands the interrelationship of human development, cognition, and culture and their impact on learning. | | | 5 | Demonstrate the ability to apply analytical and theoretical skills to model and solve mathematical problems. | P | | 6 | Demonstrate the ability to effectively use a variety of teaching technologies and techniques and classroom strategies to positively influence student learning. | | | 7 | Understands how to form connections among educators, families, and the larger community to promote equity and access to education for his/her students. | | | 8 | Understands assessment and evaluation of student performance and learning and program effectiveness. | | | 9 | Communicates effectively and works collaboratively within the context of a global society. | |
|
| Prerequisites (Course Reading List and References): | Advanced Calculus I-II and Mathematical Analysis I-II |
| Student's obligation (Special Requirements): | students are obligated to follow all lectures and to take notes from the board. The usage of all kind of electronic devices are forbidden. |
| Course Book/Textbook: | Introductory Functional Analysis with applications,Kreyszig University of Windsor |
| Other Course Materials/References: | lecture notes PPTs |
| Teaching Methods (Forms of Teaching): | Lectures, Practical Sessions, Excersises, Presentation, Self Evaluation, Assignments, Demonstration |
COURSE EVALUATION CRITERIA
| Method | Quantity |
Percentage (%) | | Participation | 1 | 5 | | Quiz | 2 | 10 | | Homework | 3 | 5 | | Midterm Exam(s) | 1 | 20 | | Final Exam | 1 | 40 |
| Total | 100 |
Examinations: Essay Questions, True-False, Fill in the Blanks, Short Answers |
|
Extra Notes:
|
ECTS (ALLOCATED BASED ON STUDENT) WORKLOAD| Activities | Quantity | Duration (Hour) | Total Work Load | | Contact Hours (Theoretical hours + Practical hours/2) x Weeks | 14 | 3 | 42 | | Hours for off-the-classroom study | 14 | 2 | 28 | | Study hours for the Midterm Exam | 8 | 4 | 32 | | Study hours for the Final Exam | 1 | 8 | 8 | | Other | | | 0 | | ECTS | 5 | | 0 | | | | 0 | | | | 0 | | Total Workload | 110 | | ECTS Credit (Total workload/25) | 4.4 |
|