COURSE UNIT TITLE

: DIFERENTIAL EQUATIONS II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 2040 DIFERENTIAL EQUATIONS II COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR MELTEM ADIYAMAN

Offered to

Mathematics (Evening)
Mathematics

Course Objective

The objective is to present qualitative aspects of ordinary differential equations by giving the existence-uniqueness and related analysis for initial value problems, autonomous equations, boundary value problems, eigenvalue problems

Learning Outcomes of the Course Unit

1   Will be able to understand the standard theorems on the existence, uniqueness of a differential equation
2   Will be able to understand the continuation, and continuity properties of solutions that apply to a wide class of ordinary differential equations
3   Will be able to know the stability properties of linear, almost linear, and nonlinear equations and how to identify these properties
4   Will be able to solve problems involving basic matrix theory including matrix algebra, eigenvalues and eigenvectors
5   Will be able to know the structure and basic theory of Boundary value Problems and eigenvalue problems.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction to theoretical aspects of ordinary differential equations, The Cauchy Euler method
2 Direction Fields, Preliminary Discussion of Existence and Uniqueness
3 Differential Inequalities, Gronwalls lemma, The Uniqueness Theorem
4 Picard s method, Proof of the Existence Theorem
5 Continuation of the solution, Dependence on the initial value
6 The existence and uniqueness of system and higher order ordinary differential equations, The corresponding integral equations of Initial value problems, Picards method
7 Continuation of the solution, dependence on parameter for the systems, complex valued equations
8 Midterm
9 General Theory of Homogeneous and non-homogeneous linear equations, The Wronskian identity and Wronskian properties
10 Autonomous equations, stability of nonlinear equations,
11 Exponential matrix, The solution of linear system by eigenvectors
12 Boundary Value Problems and the number of solutions of Boundary value problems
13 Eigenvalue problems, Regular Sturm Liouville Boundary value problems
14 The Sturm Comparison Theorem

Recomended or Required Reading

Textbook(s): "Fundamentals of Differential Equations and Boundary Value Problems (fifth edition) by Nagle, Saff and Snider, Pearson,Addison Wesley
Supplementary Book(s): Elementary differential equations and Boundary value problems, William E. Boyce, RichardC. Diprima, John Wiley &Sons (Seventh edition)
Materials: Course presentation slayts

Planned Learning Activities and Teaching Methods

Lecture Notes
Presentations
Solving Problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + FIN * 0.60


*** 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

1. Attending at least 70 percent of lectures is mandatory.
2. Plagiarism of any type will result in disciplinary action

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
Tutorials 13 1 13
Preparations before/after weekly lectures 12 4 48
Preparation for midterm exam 1 30 30
Preparation for final exam 1 40 40
Preparation for quiz etc. 0 0 0
Final 1 2 2
Midterm 1 2 2
Quiz etc. 0 0 0
TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1324344
LO.2435254
LO.3445254
LO.454554
LO.554554

CONTACT INFORMATION
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