Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course To learn the fundemantal concepts about the dynamical systems
Course Content One-dimensional dynamical systems, fixed points
and their stabilities. Population growth model, Linear Stability analysis, Existence and Uniqueness of differential equations. Potential functions. Bifurcations, Two dimensional dynamical systems, classification of linear systems, Phase plane, fixed points and linearization, conservative systems, reversible systems, pendulum, limit cycles, Gradient systems, Liapunov functions, Poincare-Bendixson theorem.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Fatih Erman
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Nolinear Dynamics and Chaos, S. H. Strogatz
Differential equatons, Dynamical systems, and Linear Algebra by M.W. Hirsch and S. Smale, Academic Press Inc. 1974

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 30
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
% 70

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 48 48
Application (Homework, Reading, Self Study etc.) 1 20 20
Exams and Exam Preparations 2 57 114
Total Work Load   Number of ECTS Credits 6 182

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To state the fundemantal concepts about the nonlinear systems
2 To identify the fundemental constructions and to learn some of the fundemental equations and theorems about nonlinear differential equations
3 To analyze the nonlinear systems and to learn the notion of sinks,source,bifurcation...etc
4 To learn the fundemantal concepts about limit cycle and Poincare-Bendixson theorem.

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction, one dimensional dynamical systems, fixed points and stability, population growth model. Main textbook
2 Linear Stability analysis, Existence and Uniqueness. Main textbook
3 Impossibility of oscillations, potential functions. Main textbook
4 Bifurcations. Main textbook
5 Bifurcations. Main textbook
6 Overdamped Bead on a Rotating hoop, singular limits. Main textbook
7 Two dimensional Flows, stability language, classification of linear systems, examples. Main textbook
8 Phase portraits. Main textbook
9 Fixed points and linearization. Main textbook
10 Lotka-Volterra model. Main textbook
11 Conservative systems, nonlinear centers. Main textbook
12 Reversible systems, pendulum. Main textbook
13 Limit cycles, Gradient systems, Liapunov functions, Main textbook
14 Poincare-Bendixson theorem. Main textbook

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4
C2 4 4 4
C3 4 4 4
C4 4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant