Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
DIFFERENTIAL EQUATIONS I 801500715370 3 + 0 3.0 8.0

Prerequisites None

Language of Instruction Turkish
Course Level Graduate Degree
Course Type Compulsory
Mode of delivery Expression, Ouestion-Answer, Discussion, Solving problem
Course Coordinator
Instructors Hüseyin BEREKETOĞLU
Assistants
Goals Introduction to the basic theory of differential equations, to prove the existence and uniqueness theorems, introduction to the concept of continuous dependence of the solutions, the study of periodic linear system, Lyapunov stability in terms of basic definitions with stability
Course Content Vector differential equations, existence and uniqueness theorems, Lipschitz condition, autonomous equations, equidimensionality, scale invariance, Riccati’s equation, second order Riccati’s equation, Abel’s equation, phase plane and Lie plane study, Duffing’s equation, Volterra-Lotka systems, Lane-Emden equation, Langmuir’s equation, the study of some nonlinear models.
Learning Outcomes 1) Learns to apply existence and uniqueness theorems.
2) Understand the basic theory of linear homogenous and inhomogeneous differential equations.
3) It makes the continuation of the solution.
4) Investigate the continuous dependence of the solution.
5) Examine the periodic linear systems.
6) To use the definitions of stability, asymptotic stability and instability for linear and nonlinear systems
7) Apply uniform stability, uniform asymptotic stability and exponential stability conditions
8) Examine the solutions of asymptotic behavior in variable coefficient of linear systems
9) To interpret the behavior of solutions of weakly nonlinear system.

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Existence and uniqueness of solutions of scalar differential equations Lecture; Question Answer
Colloquium
Brain Based Learning 		Homework
2. Week Peano's and Caratheodory's existence theorems Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
3. Week Maximal and minimal solutions, continuation of solutions Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
4. Week Existence and uniqueness theorems for systems of differential equation Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
5. Week Peano existence theorem for vector condition and continuation solutions Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
6. Week ε- approximate solutions, the Cauchy-Peano existence theorem Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
7. Week Differential and integral inequalities Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
8. Week Applications: Zieba's theorem, Perron criterion Kamke uniqueness theorem, criteria of Naguma, Osgood criteria Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
9. Week Banach fixed point theorem Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
10. Week Schander fixed point theorem, Tychanov fixed-point theorem, local and global theorems Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
11. Week Homogeneous linear systems and properties, basic matrix, Abel-Liouville formula Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
12. Week Adjoint systems, periodic linear systems, Floquet theorem Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
13. Week Linear non-homogeneous systems, formula of variation of constants, asymptotic behavior Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework
14. Week Behaviour of solutions of n-th order linear scalar homogeneous equations, Hurwitz theorem Lecture; Question Answer; Problem Solving
Colloquium
Brain Based Learning 		Homework

Sources Used in This Course
Recommended Sources
Bruce P. Conrad, Differential Equations, Prentice Hall, 2003.
D.K. Arrowsmith, C.M. Place, An Introduction to Dynamical Systems, Cambridge University Press, 1990.
Hüseyin BEREKETOĞLU, Diferensiyel Denklemler, Nobel, 2021
John Polking, Albert Bogess, David Arnold, Differential Equations, Prentice Hall, New Jersey, 2001.
M. Rama Mohana Rao, Ordinary Differential Equations Theory and Applications, Edward Arnold, 1981.
R.A. Struble, Nonlinear Differential Equations, McGraw-Hill Co. 1962.
S.G. Deo, V. Raghavendra, Ordinary Differential Equations and Stability, Tata McGraw-Hill Publishing Company, 1988.
Stanley J. Farlow, Differential Equations and Their Applications, McGraw-Hill Co., 1994.

Relations with Education Attainment Program Course Competencies
Program RequirementsContribution LevelDK1DK2DK3DK4DK5DK6DK7DK8DK9
PY15000000000
PY25000000000
PY35000000000
PY45000000000
PY43434343434
PY45454554550
PY45545454550
PY45333433430
PY45000000000
PY45555555555
PY45000000000
PY45555555555
PY45555555555
PY45000000000
PY45000000000
PY45555555555
PY45555555555

*DK = Course's Contrubution.
0 1 2 3 4 5
Level of contribution None Very Low Low Fair High Very High
.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 3
Work Hour outside Classroom (Preparation, strengthening) 14 3
Homework 3 10
Midterm Exam 1 2
Time to prepare for Midterm Exam 1 55
Final Exam 1 2
Time to prepare for Final Exam 1 65
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
Quick Access Hızlı Erişim Genişlet
Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • Relations with Education Attainment Program Course Competencies
  • ECTS credits and course workload