COURSE UNIT TITLE

: DIFFERENTIAL EQUATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
FIZ 2109 DIFFERENTIAL EQUATIONS ELECTIVE 2 2 0 6

Offered By

Physics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR YUSUF YÜKSEL

Offered to

Physics

Course Objective

Audience of the course is undergraduate student in the 3th semester. Theory of differential equations is partly introduced in mathematical methods in physics lectures. This lecture focuses on the theoretical background of differential equations which are familiar to physics students. The students who successfully complete the lecture will gain the ability of an analytical approach to fundamental physical problems, in addition to the mathematical experience for the advanced topics of physics.

Learning Outcomes of the Course Unit

1   To learn the methods of solutions for the first order ODEs.
2   To learn the methods of solutions for the second order ODEs.
3   To learn the basics and solution methods of systems of differential equations and related physical problems.
4   To gain information on the solution methods of partial differential equations.
5   To set a relation between the special differential equations and their applications in physics.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 First order ODEs: Fundamental concepts, Euler s method, modelling
2 First order ODEs: Integrating factors, Bernoulli s equation and population dynamics
3 Second order ODES: Homogeneous equations with constant coefficients, differential operators, mass-spring system
4 Second order ODES: Euler-Cauchy equations, Wronskian, non-homogenous equations
5 Second order ODES: non-homogenous equations, forced oscillations and resonance, electric circuits
6 Systems of ODEs: Matrix and vector algebra, physical applications
7 Topical Review & Problem Solution
8 Solutions with Series Method
9 Series solutions of ODEs: Legendre s equation
10 Series solutions of ODEs: Bessel s equation
11 Solutions with Laplace transforms, Fourier analysis
12 Partial differential equations: wave equation in 1D and 2D
13 Partial differential equations: heat equation in 1D and 2D
14 Topical Review & Problem Solution

Recomended or Required Reading

Advanced Engineering Mathematics (10th edition), E. Kreyszig, Wiley 2011

Auxiliary textbook
A first course in differential equations with modeling applications (10th edition),, D. G. Zill Brooks/Cole 2011
Material:
- Schaum s Outlines, Differential Equations (fourth edition),, McGrawHill

Planned Learning Activities and Teaching Methods

Lectures, problem solving and discussion, Tutorials and homeworks

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


Further Notes About Assessment Methods

None

Assessment Criteria

The student s performance will be according to the midterm and final exam grade, as well as the homework assigments.

Language of Instruction

Turkish

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)

yusuf.yuksel@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 2 28
Tutorials 14 2 28
Preparations before/after weekly lectures 14 2 28
Preparation for midterm exam 1 14 14
Preparation for final exam 1 14 14
Preparing assignments 0 0 0
Midterm 1 14 14
Final 1 14 14
TOTAL WORKLOAD (hours) 140

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.155554444353222
LO.255554444353222
LO.355554444353222
LO.455554444353222
LO.555554444353222

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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