COURSE UNIT TITLE

: THEORY OF LINEAR UNBOUNDED OPERATORS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6026 THEORY OF LINEAR UNBOUNDED 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 (English)
Mathematics (English)

Course Objective

It aims to develop the abstract methods of functional analysis which can be applied to the
problems of mathematical physics.

Learning Outcomes of the Course Unit

1   will be able to understand the concept of an unbounded operator.
2   will be able to distinguish between adjoint and symmetric operators.
3   will be able to understand the concept of a Closed Operator.
4   will be able to understand the Cayley Transform.
5   will be able to understand the Spectral Theory of unbounded self-adjoint linear operators.

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 Unbounded linear operators and their Hilbert Adjoint Operators.
3 Symmetric and Self-adjoint Operators
4 Closed Linear Operators and Closures
5 Spectrum of unbounded operators
6 Unitary Operators and Cayley Transform
7 Spectral Theorem for Unbounded Self -adjoint Linear Operators
8 Quadratic forms.
9 Extension of Symmetric Operators.
10 Cayley Transform for Symmetric Operators
11 Deficiency indices
12 Functional Calculus
13 Continuous Perturbations
14 Analytic Perturbations

Recomended or Required Reading

Textbook(s):
Introductory to Functional Analysis with Applications, Erwin Kreyszig, John Wiley & Sons, 1978.
Functional Analysis, Riesz, Nagy, Dover
Supplementary Book(s):
Functional Analysis, Peter D. Lax, Wiley & Sons.

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


Further Notes About Assessment Methods

None

Assessment Criteria

%30(mte)+%20(asg)+%50(final)

Language of Instruction

English

Course Policies and Rules

You can be successful in this course by studying from your textbooks and lecture
notes on the topics to be covered every week, coming to class by solving the given
problems, establishing the concepts by discussing the parts you do not understand
with your questions, learning the methods, and actively participating in the course.

Contact Details for the Lecturer(s)

sedef.erim@deu.edu.tr

Office Hours

to be announced later

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 6 84
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) 202

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.155555555
LO.255555555
LO.355555555
LO.455555555
LO.555555555

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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