1. SECOND CYCLE - MASTER'S DEGREE
  2. THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
  3. MATHEMATICS DEPARTMENT
  4. 1441 Mathematics
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 541FUNCTIONAL ANALYSIS II3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective The aim of this course is to provide an introduction to Spectral Theory by investigating concepts of compact linear operator, bounded and unbounded linear operators.
Course Content Spectral Theory of Linear Operators on Normed Spaces, Compact Linear Operator and Its Spectrums, Spectral Theory of Bounded Self-Adjoint Operators, Unbounded Linear Operators on Hilbert Spaces.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.

COURSE LEARNING OUTCOMES
1Knows Spectral Theory of Linear Operators on Normed Spaces.
2Learns Compact Linear Operator and Its Spectrums.
3Recognizes the Spectral Theory of Bounded Self-Adjoint Operators.
4Learns the structure of Unbounded Linear Operators on Hilbert Spaces.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0015  44   
LO 0024 54    
LO 003   454  
LO 0045  54   
Sub Total14 517134  
Contribution40143100

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course





195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2025-2026 Fall1ALP ARSLAN KIRAÇ


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester Mode of Delivery
MAT 541 FUNCTIONAL ANALYSIS II 3 + 0 1 Turkish 2025-2026 Fall Face to Face
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. ALP ARSLAN KIRAÇ aakirac@pau.edu.tr FEN A0203 %80
Goals The aim of this course is to provide an introduction to Spectral Theory by investigating concepts of compact linear operator, bounded and unbounded linear operators.
Content Spectral Theory of Linear Operators on Normed Spaces, Compact Linear Operator and Its Spectrums, Spectral Theory of Bounded Self-Adjoint Operators, Unbounded Linear Operators on Hilbert Spaces.
Topics
WeeksTopics
1 Linear Differential Expressions
2 Homogeneous Boundary-Value Problem
3 Lagrange Formula
4 Adjoint Differential Expressions
5 Adjoint Boundary-Value Problem
6 Eigenvalue and Eigenvectors of Differential Operators
7 Green's Function for Linear Differential Operator
8 Asymptotic Behaviour of Eigenvalue and Eigenvectors
9 Midterm
10 Analytical Structure of Green Functions
11 Regular Boundary-Value Problems
12 Spectral Expansion of Differential Operators belong to Regular Boundary Conditions
13 Operators that Produced by Self-adjoint Differential Expressions for Singular Situation
14 Self-adjoint Extension of Symetric Differential Operators, Inverse Spectral Problems of Ordinary Differential Operators.
Materials
Materials are not specified.
Resources
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