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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6025 FUNCTIONAL ANALYSIS 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

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 fundamental theorems of functional analysis: Banach Theorem, Open Mapping Theorem, Uniform Boundedness Theorem. 2   will be able to understand Riesz Theorem. 3   will be able to distinguish between weak convergence, strong convergence and uniform convergence. 4   will be able to use the spectral properties of a self adjoint compact operator. 5   will be able to understand Spectral family, spectral representations of bounded self-adjoint operators.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Metric Spaces. Banach spaces. Hilbert Spaces. Seperable space. 2 Hahn Banach Theorem(s) and its applications 3 Strong,weak convergence, Uniform Boundednes Theorem 4 Open Mapping Theorem, Closed Graph Theorem. 5 Spectral Theory . 6 Compact Operators and their Spectrum 7 Application of spectral theory of compact operators 8 MIDTERM 9 Spectral properties of a bounded self adjoint linear operator 10 Positive operators. 11 Square roots of positive operators 12 Projection Operators. 13 Spectral family of a bounded self adjoint linear operator 14 Spectral representation of a bounded self adjoint linear operator

Recomended or Required Reading

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

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