Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
SYSTEMS OF DIFFERENTIAL EQUATIONS MAT4413 0 + 0 3.0 6.0

Prerequisites None

Language of Instruction English
Course Level Graduate Degree
Course Type Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals The aim of this course is to define differential equations systems, to teach existence and uniqueness theorems and solving methods for systems of differential equations, to investigate Hamiltonian systems.
Course Content Existence and uniqueness theorems, n-dimension linear differential equations systems, matrix method, linear systems with periodic coefficients, nonlinear differential equations systems, Hamiltonian systems.
Learning Outcomes 1) Explains the relationship between systems of differential equations and dynamical systems.
2) Uses the existence and uniqueness theorems for initial value problems.
3) Calculates the eigenvalues ​​and eigenvectors of systems of linear equations
4) Implements the operator method and the matrix method.
5) Examine the properties of systems of linear differential equations with periodic coefficients.
6) Applies the Floquet theory.
7) Finds the general solution of nonlinear differential systems by calculating the first integrals.
8) Recognizes the Hamilton systems.
9) Calculates the Hamilton function.

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Basic theory for differential equations systems Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
2. Week Scalar differential equations; Existence and Uniqueness Theorems Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
3. Week Existence and Uniqueness Theorems for systems of differential equations Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
4. Week The Method of Succesive Approximations Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
5. Week The Operator Method Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
6. Week Solutions of linear systems: Two equations in two unknown functions Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
7. Week Mid-term exam Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
8. Week Nonhomogeneous linear systems: Two equations in two unknown functions-Basic Theory of Linear Systems Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
9. Week Eigenvalues, Eigenvectors Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
10. Week The Matrix Method Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
11. Week The method of variation of parameters Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
12. Week Linear systems with periodic coefficients Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
13. Week Nonlinear differential equations systems and first integrals Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework
14. Week Hamiltonian systems Lecture; Question Answer; Problem Solving
Brainstorming
Problem Based Learning 		Homework

Sources Used in This Course
Recommended Sources
G. F. Simmons, Differential Equations, Tata McGraw Hill, 1989.
Lawrence Perko, Differential Equations and Dynamical Systems, Springer, 2001.
P.N.V. Tu, Dynamical Systems, springer-Verlag, 1994.
R.E. Williamson, differential Equations and Dynamical Systems, McGraw Hill, 2001.
Shepley L.ROSS,Differential Equations,Third Edition,John Wiley and Sons,Inc.,New York,1984.
William E. Boyce, Richard C. DiPrima, Elemantary Differential Equations and Boundary Value Problems, John Wiley and Sons, Inc., New York, 2005.

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 4 2
Midterm Exam 1 2
Time to prepare for Midterm Exam 1 30
Final Exam 1 2
Time to prepare for Final Exam 1 40
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
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Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • ECTS credits and course workload