• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Generalize, Empasize and Apply the concept of Nonlinear Analysis for Dynamic Systems

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Work effectively in multi-disciplinary research teams
   6. Design and conduct research projects independently
   7. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   8. Develop mathematical, communicative, problem-solving, brainstorming skills.
   9. Effectively express his/her research ideas and findings both orally and in writing

   Method of assessment

   1. Written exam
2. Explain and Apply the principles of Nonlinear Analysis for Dynamic Systems

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Work effectively in multi-disciplinary research teams
   6. Design and conduct research projects independently
   7. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   8. Develop mathematical, communicative, problem-solving, brainstorming skills.

   Method of assessment

   1. Oral exam
   2. Homework assignment
3. Interpret the Stability results and Applications of Dynamical Systems

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Work effectively in multi-disciplinary research teams
   6. Design and conduct research projects independently
   7. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   8. Develop mathematical, communicative, problem-solving, brainstorming skills.

   Method of assessment

   1. Oral exam
   2. Seminar/presentation
   3. Term paper

Contents
Week 1:	Linear Variation of Paremeters for Dynamical Systems.
Week 2:	Nonlinear VPs.
Week 3:	VPs formulae in terms of Lyapunov-like functions.
Week 4:	Boundary value problems.
Week 5:	Monotone iterative technique.
Week 6:	Exponential dichotomy. Midterm Exam I.
Week 7:	Sensitivity analysis.
Week 8:	Existence of almost periodic solutions.
Week 9:	Stability and asymptotic behaviour.
Week 10:	Growth properties of solutions.
Week 11:	Controllability.
Week 12:	Variational comparison results for dynamic systems. Midterm Exam II.
Week 13:	Variational comparison results for dynamic systems.
Week 14:	Boundedness; controllability; Variational comparison results for dynamic systems.
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	Stability Analysis of Nonlinear Systems by V. Lakshmikantham, S. Leela and M.M.Marthnyuk.
Recommended readings:	Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	6, 12	40
Other in-term studies:	8	5
Project:	13	5
Homework:	2,3,4,7,8,9,10,13,14,15	5
Quiz:	5, 11	5
Final exam:	16	40
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	3	14
Practice, Recitation:	0	0
Homework:	6	10
Term project:	10	2
Term project presentation:	1	1
Quiz:	1	2
Own study for mid-term exam:	10	1
Mid-term:	2	2
Personal studies for final exam:	10	1
Final exam:	2	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)