PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 573	SPECTRAL THEORY OF LINEAR DIFFERENTIAL OPERATORS	3 + 0	1st Semester	7,5

COURSE DESCRIPTION

Course Level	Master's Degree
Course Type	Elective
Course Objective	The aim of this course is to provide an introduction to the basic concepts used in Spectral Theory of Linear Differetial Operators described in the course contents.
Course Content	Linear Differential Expressions, Homogeneous Boundary-Value Problem, Lagrange Formula, Adjoint Differential Expressions, Adjoint Boundary-Value Problem, Eigenvalue and Eigenvectors of Differential Operators, Green's Function for Linear Differential Operator, Asymptotic Behaviour of Eigenvalue and Eigenvectors, Analytical Structure of Green Functions, Regular Boundary-Value Problems, Spectral Expansion of Differential Operators belong to Regular Boundary Conditions, Operators that Produced by Self-adjoint Differential Expressions for Singular Situation, Self-adjoint Extension of Symetric Differential Operators, Inverse Spectral Problems of Ordinary Differential Operators.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.
Mode of Delivery	Face to Face

COURSE LEARNING OUTCOMES

1	Understands linear differential expressions , Adjoint differential expressions , Adjoint boundary value problem, Eigenvalue and eigen function of differential operators.
2	Learns the classification of regular boundary value problems.
3	Comments asymptotic behavior of eigenvalue and eigenvectors.

COURSE'S CONTRIBUTION TO PROGRAM

	PO 01	PO 02	PO 03	PO 04	PO 05	PO 06	PO 07	PO 08
LO 001	5		4	5
LO 002	4		5		4
LO 003	5		4		4
Sub Total	14		13	5	8
Contribution	5	0	4	2	3	0	0	0

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	7	98
Assignments	1	5	5
Mid-terms	1	15	15
Final examination	1	35	35
Total Work Load ECTS Credit of the Course			195 7,5

COURSE DETAILS

Select Year

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester
MAT 573	SPECTRAL THEORY OF LINEAR DIFFERENTIAL OPERATORS	3 + 0	1	Turkish	2020-2021 Spring

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. ALP ARSLAN KIRAÇ	aakirac@pau.edu.tr		FEN A0210	%

Goals		The aim of this course is to provide an introduction to the basic concepts used in Spectral Theory of Linear Differetial Operators described in the course contents.
Content		Linear Differential Expressions, Homogeneous Boundary-Value Problem, Lagrange Formula, Adjoint Differential Expressions, Adjoint Boundary-Value Problem, Eigenvalue and Eigenvectors of Differential Operators, Green's Function for Linear Differential Operator, Asymptotic Behaviour of Eigenvalue and Eigenvectors, Analytical Structure of Green Functions, Regular Boundary-Value Problems, Spectral Expansion of Differential Operators belong to Regular Boundary Conditions, Operators that Produced by Self-adjoint Differential Expressions for Singular Situation, Self-adjoint Extension of Symetric Differential Operators, Inverse Spectral Problems of Ordinary Differential Operators.

Topics

Weeks	Topics
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 Methods	Percentage (%)	Assesment Methods Title
Final Exam	50	Final Exam
Midterm Exam	50	Midterm Exam

L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

Prospective Student