11111

COURSE INTRODUCTION AND APPLICATION INFORMATION


umi.fbe.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Fall
Prerequisites
None
Course Language
Course Type
Required
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Case Study
Q&A
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be able to analyze, transform, use in the models and solve the second order differential equations
  • will be able to solve Systems of Linear differential equations.
  • will be able to analyze the methods of nonlinear differential equations.
  • will be able to solve Hamiltonian Systems.
  • will be able to determine Stability of linear and nonlinear systems.
Course Description

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Second-order differential equations in the phase plane Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
2 Conservative system Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
3 Some applications and graphical representation of solutions Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
4 Plane autonomous systems and linearization Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
5 Plane autonomous systems and linearization Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
6 Limit cycles Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
7 Periodic solutions Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
8 Perturbation methods Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
9 Perturbation methods Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
10 Poincare stability Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
11 Lyapunov methods for the stability Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
12 Bendixson's theorem. Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
13 Hamiltonian systems Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
14 Seminars Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
15 Seminars Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
16 Review of the Semester  
Course Notes/Textbooks Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
Suggested Readings/Materials Elementary Differential Equations by Boyce and DiPrima; Wiley. Ementary Differential Equations with Boundary Value Problems by Edwards and Penney; Prentice Hall. An Introduction to Dynamical Systems, by Alligood, Sauer, and Yorke, Springer.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
1
20
Oral Exam
Midterm
1
40
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
6
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
1
20
Project
Seminar / Workshop
1
Oral Exam
Midterms
1
42
Final Exams
1
45
    Total
245

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

İzmir Ekonomi Üniversitesi | Sakarya Caddesi No:156, 35330 Balçova - İZMİR Tel: +90 232 279 25 25 | webmaster@ieu.edu.tr | YBS 2010