COURSE UNIT TITLE

: THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5017 THEORY OF 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

ASSOCIATE PROFESSOR MELTEM ADIYAMAN

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to learn the uniqueness and existence theorems of ordinary differential equations, linear systems of equations and their approximate solutions

Learning Outcomes of the Course Unit

1   will be able to understand the basic theory of ordinary differential equations.
2   will be able to apply the Cauchy-Euler approximation method.
3   will be able to understand and use the theorems on uniqueness and existence for solutions.
4   will be able to understand the theory for solving systems and linear systems of differential equations.
5   will be able to understand the theory for solving autonomous and nonlinear systems.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Fundamentals, The Cauchy-Euler approximation method, Fundamental inequality
2 Uniqueness and existence theorems
3 Solutions containing parameters
4 Continuation of solutions, Dependence of solutions on initial conditions and parameters, Other method of solutions
5 System of differential equations, Approximate solutions, The Lipschitz conditions, Fundamental inequality
6 Existence and properties of solutions of the system
7 Midterm, Systems of higher order
8 Linear systems of differential equations, Solutions of systems of differential equation in matrix form, Reduction of order of a system
9 Nonhomogeneous systems
10 Linear equations of higher order, Reduction of order, Nonhomogeneous case
11 Greens function
12 Linear systems with constant coefficients, Complex solutions
13 Singularities of an autonomous system
14 Nonlinear systems

Recomended or Required Reading

1. Witold Hurewicz, Lectures on Ordinary Differential Equations, The M.I.T. Press, Massachusetts Institue of Technology, 1958
2. Earl A. Coddington and Norman Levinson, Theory of Ordinary Differential Equations, McGraw Hill, 1955
3. Shepley L. Ross, Introduction to Ordinary Differential Equations, Blaisdell Publishing Company, New York, 1966
4. Morris W. Hirsch and Stephen Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, 1974

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation, Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

Assignment, Midterm, Final

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

meltem.evrenosoglu@deu.edu.tr

Office Hours

To be announced...

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparation for midterm exam 1 35 35
Preparation for final exam 1 40 40
Preparing assignments 7 7 49
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 172

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.15
LO.25
LO.33
LO.45
LO.54

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

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