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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5034 ADVANCED ORDINARY DIFFERENTIAL EQUATIONS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics Mathematics

Course Objective

The purpose of this course is to study stability, asymptotic behaviour, and boundary value problems in the theory of differential systems

Learning Outcomes of the Course Unit

1   will be able to know an appreciation of some of the central ideas of ordinary differential equations such as the role of lipshitz conditions and compactness in existence theory 2   will be able to apply theory to the analysis of concrete model problems, 3   will be able to establish existence of solutions including periodic solutions 4   will be able to establish stability of solutions 5   will be able to understand the functional analysis treatments of various aspects of nonlinear analysis

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Banach spaces, Bounded Linear Operators 2 Fixed point Theorems, Banach Contraction Principle, The Schauder-Tychonov Theorem, The Leray-Schauder Theorem, The inverse Function Theorem 3 Existence and Uniqueness, Continuation, 4 Basic Theory of Linear Systems 5 Stability of linear systems 6 Perturbed Linear Systems 7 Midterm 8 Lyapunov Functions in the theory of differential equation 9 Comparison principle and Stability 10 Boundary value problems on Finite intervals 11 Periodic solutions of linear systems 12 Monotocity, a more general inner product,stability regions 13 Boundary value problems on infinite intervals 14 Problems on infinite intervals

Recomended or Required Reading

Athanassios G. Kartsatos, Advanced Ordinary Differential Equations, 1993

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Homeworks

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 * 0.20 + ASG * 0.40 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.20 + ASG * 0.40 + RST * 0.40 *** 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

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

sennur.somali@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 3 39 Preparation for final exam 1 25 25 Preparing assignments 10 5 50 Preparation for midterm exam 1 15 15 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 174

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 4 3 3 4 2 3 3 3 3 3 LO.2 4 4 4 5 4 5 2 4 2 4 3 LO.3 4 4 4 5 4 4 2 4 2 4 3 LO.4 4 4 4 5 4 4 2 4 2 4 4 LO.5 5 5 5 5 5 5 5 3 4 4