Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT507 - MATHEMATICS

Code: MAT507 Course Title: FUNCTIONAL ANALYSIS AND APPLICATIONS I Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Fall Semester
Level of Course 2nd Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer ZARİFE ZARARSIZ (zarifezararsiz@nevsehir.edu.tr)
Name of Lecturer(s)
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course

Learning Outcomes PO MME
The students who succeeded in this course:
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Metric Spaces Oral presentation, question and answer, problem solving
2 Open set, closed set, neighborhood concepts Oral presentation, question and answer, problem solving
3 Convergence, Cauchy sequence, completeness concept Oral presentation, question and answer, problem solving
4 proofs of completeness Oral presentation, question and answer, problem solving
5 Complementing metric spaces Oral presentation, question and answer, problem solving
6 Vector spaces Oral presentation, question and answer, problem solving
7 Normed spaces and Banach spaces Oral presentation, question and answer, problem solving
8 mid-term exam
9 Finite-dimensional normed spaces and subspaces Oral presentation, question and answer, problem solving
10 Compactness and finite dimensional(size) Oral presentation, question and answer, problem solving
11 Linear operators Oral presentation, question and answer, problem solving
12 Bounded and continuous linear operators Oral presentation, question and answer, problem solving
13 Linear functionals Oral presentation, question and answer, problem solving
14 Linear operators and functionals in finite dimensional spaces Oral presentation, question and answer, problem solving
15 Normed operator spaces, dual space Oral presentation, question and answer, problem solving
16 final exam
Recommend Course Book / Supplementary Book/Reading
Required Course instruments and materials

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 14 42
Outside Class
       a) Reading 5 14 70
       b) Search in internet/Library 2 14 28
       c) Performance Project 0
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 4 4 16
mid-term exam 2 1 2
Own study for final exam 5 4 20
final exam 2 1 2
0
0
Total work load; 180