Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
INTRODUCTİON TO FUNCTIONAL ANALYSIS MAT3378 0 + 0 3.0 4.0

Prerequisites None

Language of Instruction Turkish
Course Level Graduate Degree
Course Type Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals To teach the notations of metric spaces normed and Banach spaces and relationship between these spaces.
Course Content Metric spaces. Vector spaces. Normed vector spaces. Banach spaces
Learning Outcomes 1) " Learns metric spaces "
2) "Learns complete metric spaces "
3) "Learns normed spaces "
4) Learns Banach spaces

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Metric spaces and examples of metric spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
2. Week Hölder and Minkowski Inequalities Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
3. Week Topology of metric spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
4. Week Separable metric spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
5. Week Convergence, Cauchy sequences and completeness Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
6. Week Teorems about completeness Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
7. Week Midterm exam

8. Week Some complete spaces, Non-complete metric spaces and completion Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
9. Week Vector spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
10. Week Normed spaces and Banach spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
11. Week Some properties of normed spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
12. Week Completion of normed spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
13. Week Finite dimensional normed spaces Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)
14. Week Equivalent norms and their topologies Lecture; Question Answer
Brainstorming
Problem Based Learning 		Homework Presentation (Including Preparation Time)

Sources Used in This Course
Recommended Sources
Erwin Kreyszig, Introductory Functional Analysis with Applications

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) 5 3
Homework 3 4
Midterm Exam 1 2
Time to prepare for Midterm Exam 1 15
Final Exam 1 2
Time to prepare for Final Exam 1 30
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
Quick Access Hızlı Erişim Genişlet
Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • ECTS credits and course workload