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

PROFESSOR DOCTOR BAŞAK KARPUZ

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 Theory of Ordinary Differential Equations, Cauchy-Euler Method
2 Direction Fields, Preliminary Discussion of Existence and Uniqueness
3 Differential Inequalities, Gronwalls lemma, Uniqueness Theorem
4 Picard's Method, Proof of Existence Theorem
5 Continuation of Solutions, Dependence on the Initial Conditions
6 Autonomous Equations, Classification of Equilibrium Points, Linearization Theorem
7 Systems and Higher-Order ODEs, Initial Value Problems, Uniqueness Theorem, Picard's Technique and Existence Theorem
8 Continuation of Solutions, Dependence on Parameters
9 Homogeneous Linear Systems, Distinct Eigenvalues, Complex Eigenvalues
10 Non-Homogeneous Linear Systems, Variation of Parameters
11 Matrix Exponential, Generalized Eigenvectors, Solving the System Using Generalized Eigenvectors
12 General Theory for Linear Differential Equations, Boundary-Value Problems
13 Eigenvalue Problems, Regular Sturm Liouville Boundary Value Problems
14 Sturm's Oscillation Theorems

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 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 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)

basak.karpuz@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 3 42
Preparation for midterm exam 1 31 31
Preparation for final exam 1 37 37
Midterm 1 2 2
Final 1 2 2
TOTAL WORKLOAD (hours) 170

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
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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