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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6028 SPECTRAL THEORY OF LINEAR DIFFERENTIAL OPERATORS ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR SEDEF KARAKILIÇ

Offered to

Mathematics Mathematics

Course Objective

It aims to study the spectral theory of ordinary linear differential operators.

Learning Outcomes of the Course Unit

1   will be able to define the Linear Differential Operator. 2   will be able to understand the principle properties of the Linear Differential Operator. 3   will be able to construct Green's function. 4   will be able to understand the asymptotic expansion of eigenvalues and eigenfunctions. 5   will be able to understand Spectral expansion of a differential operator.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Review of basic concepts 2 Linear differential expressions Homogeneous Boundary Value Problem 3 Lagrange `s Formula 4 The Adjoint Differential Expression 5 The Adjoint Boundary Value Problem 6 Eigenvalues and eigenfunctions of differential operators 7 Green's Function for a linear differential operator. Asymptotic behaviour of eigenvalues and eigenfunctions 8 MIDTERM 9 Analytic nature of Green's Function 10 Regular Boundary Value Problems 11 Spectral expansion of a differential operator with regular boundary conditions 12 Operators generated by self-adjoint differential expressions in singular case 13 Self adjoint extension of the symmetric differential operators 14 On the inverse spectral problems of ordinary differential operators

Recomended or Required Reading

Textbook(s): Linear Differential Operators, M. A. Naimark Supplementary Book(s): Spectral Theory and Differential Operators, Davies, E.B. Cambridge University Press, 1995 References: Materials:

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE * 0.30 +ASG * 0.20 +FIN * 0.50 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.20 + RST * 0.50 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

sedef.erim@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 6 78 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 1 20 20 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 193

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 5 5 5 5 5 5 LO.2 5 5 5 5 5 5 5 5 LO.3 5 5 5 5 5 5 5 5 LO.4 5 5 5 5 5 5 5 5 LO.5 5 5 5 5 5 5 5 5