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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 MIDTERM 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 *** 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