Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
DMB0019		Dynamical Systems	3/0/0	DE	Turkish	7

Course Goals	The goal of the course is to give to the students a basic knowledge about dynamical systems and a qualitative insight to differential equations.
Prerequisite(s)	None
Corequisite(s)	None
Special Requisite(s)	The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)	Assist. Prof. Dr. Hikmet Çağlar
Course Assistant(s)
Schedule	Day, hours, XXX Campus, classroom number.
Office Hour(s)	Instructor name, day, hours, XXX Campus, office number.
Teaching Methods and Techniques	-Lecture
Principle Sources	-S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos, Springer,2003. -K.T.Alligood, T.D. Sauer, J.A.Yorke, Chaos(An Introduction to Dynamical Systems), Springer,1996.
Other Sources	G.Teschl, Ordinary Differential Equations and Dynamical Systems, Springer,2009.   M. Hirsh, S. Smale, R. Devaney, Differentail equations,dynamical systems and an introduction to chaos, Elsevier, 2004.   C. Robinson, Dynamical Systems, CRC, 2nd edition,1999.

Course Schedules
Week	Contents	Learning Methods
1. Week	Discrete Dynamical Systems. Population Growth Model.	Lecture
2. Week	Linear Dynamical Systems.	Lecture
3. Week	Arnold’s Cat Map. Baker’s Map. Circle Map. Henon Map. Horseshoe Map. Logistic Map. Duffing Map. Complex Quadratic Map.	Lecture
4. Week	Arnold’s Cat Map. Baker’s Map. Circle Map. Henon Map. Horseshoe Map. Logistic Map. Duffing Map. Complex Quadratic Map.	Lecture
5. Week	Fixed Points. Periodic Points. Graphical iteration and Stability.	Lecture
6. Week	Review of basic concepts and theorems in ODE. Vector fields, flows, linear systems, stability.	Lecture
7. Week	Review of basic concepts and theorems in ODE. Vector fields, flows, linear systems, stability.	Lecture
8. Week	Floquet Theorem. Logarithm of the matrix.	Lecture
9. Week	Mid Term	Mid Term
10. Week	Poincare Maps. Examples. Duffing Equation.	Lecture
11. Week	Poincare Maps. Examples. Duffing Equation.	Lecture
12. Week	Equivalence of Linear Systems. Harman-Grobman’ s Theorem.	Lecture
13. Week	Poincare- Bendixson Theorem	Lecture
14. Week	Normal Forms	Lecture
15. Week
16. Week
17. Week

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	1	40
Homework / Term Projects / Presentations	2	20
Final Exam	1	40

Program Outcomes PO-1 Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making. PO-2 Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas. PO-3 Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process. PO-4 Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written. PO-5 Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals. PO-6 Use computer software to solve problems effectively by following the developments in information and communication technologies. PO-7 Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values. PO-8 To solve problems related to the field, establish functional interacts by using strategic decision making processes. PO-9 Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.

Learning Outcomes LO-1 Has general knowledge about dynamic systems. LO-2 It comes to a level where you can do more in-depth research on dynamic systems. LO-3 Gains qualitative perspective on differential equations. LO-4 Academic studies have the level to do.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9