1. FIRST CYCLE - BACHELOR'S DEGREE
  2. FACULTY OF SCIENCE AND LETTERS
  3. MATHEMATICS DEPARTMENT
Course Information Course Learning Outcomes Course's Contribution To Program ECTS Workload Course Details
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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 430INTRODUCTION TO FUNCTIONAL ANALYSIS4 + 07th Semester8

COURSE DESCRIPTION
Course Level Bachelor's Degree
Course Type Compulsory
Course Objective The aim of this course is to provide an introduction to Functional Analysis by investigating metric and normed spaces.
Course Content Set and Relation, Metric Space and Complete Metric Space, Normed Space and Banach Space, Finite Dimensional Normed Spaces, Compactness and Finite Dimension .
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns the concepts of metric spaces, convergence, cauchy sequence, completeness and completeness of metric space.
2Learns the fundemental properties o the vector spaces, normed vector spacas.
3Learns completeness of normed spaces, have information about the complete and noncomplete normed spaces.
4Learns the relations between these spaces.
5Gains skills on the fundemental theorems of the functional analysis and problem solving skills.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09PO 10
LO 001 44  4 4  
LO 002 4   3 5  
LO 003 4   435  
LO 004 3   4445 
LO 005 44     5 
Sub Total 198  1571810 
Contribution0420031420

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14456
Hours for off-the-classroom study (Pre-study, practice)14228
Mid-terms16060
Final examination16464
Total Work Load

ECTS Credit of the Course





208

8
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2020-2021 Fall1ALP ARSLAN KIRAÇ


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 430 INTRODUCTION TO FUNCTIONAL ANALYSIS 4 + 0 1 Turkish 2020-2021 Fall
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. ALP ARSLAN KIRAÇ aakirac@pau.edu.tr FEN A0313 %70
Goals The aim of this course is to provide an introduction to Functional Analysis by investigating metric and normed spaces.
Content Set and Relation, Metric Space and Complete Metric Space, Normed Space and Banach Space, Finite Dimensional Normed Spaces, Compactness and Finite Dimension .
Topics
WeeksTopics
1 Set and Relation, Metric Space, Further Examples of Metric Spaces
2 Open Set, Closed Set, Neighborhood, Continuity
3 Accumulation Point and Closure of a Set, Separable Space
4 Topological Spaces, Neighborhood and Continuity in Topological Spaces, Sequentially Continuity
5 Convergence of a Sequence in Metric Spaces, Cauchy Sequence, Complete Metric Space
6 Completion of Metric Spaces
7 Linear Space, Linear Subspace, Hamel Basis
8 Normed Space, Banach Space
9 Midterm Exam
10 Function Spaces, Uniform Convergence
11 Finite Dimensional Normed Spaces, Equivalent Norms
12 Compactness and Finite Dimension
13 Totally Bounded Sets
14 Banach Fixed Point Theorem and Applications
Materials
Materials are not specified.
Resources
ResourcesResources Language
FONKSİYONEL ANALİZ-MUSTAFA BAYRAKTARTürkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes