APPLIED MATHEMATICS (TURKISH, NON-THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5011 Differential Equations I Fall 3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. CANAN ÇELİK KARAASLANLI
Recommended Optional Program Components: None
Course Objectives: 1. To learn and solve the linear systems
2. To understand the stability of the linear systems
3. To learn the fundamental Existence and Uniqueness theorem
4. To learn the local theory of dynamical systems

Learning Outcomes

The students who have succeeded in this course;
At the end of the course students will have the knowledge on the following conscepts and their applications
I. Linear systems, exponential of operators, complex eigenvalues
II. The Fundamental existence-uniqueness theorem
III. Local theory of Dynamical systems
IV . The stable manifold theorem
V. The Hartman-Grobman theorem
VI. Stability and Liapunov functions
VII.Gradient and Hamiltonian systems

Course Content

Linear Systems, Stability Thoery, The Fundamental Existence and Uniqueness Theorem, Local Theory of Dynamical Systems, The Stable Manifold Theorem, The Hartman-Grobman Theorem

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Linear Systems, Uncoupled Linear Systems
2) Exponential of Operators, Linear Systems in R^2
3) Complex Eigenvalues, Stability Theory
4) Stability Thoery, Nonhomogeneous Linear Systems
5) Some Preliminaries Concepts and Definitions, The Fundamental Existence and Uniqueness Theorem
6) Dependence on Initial Conditions and Parameters
7) The maximal Interval of Existence
8) Local Theory of Dynamical Systems
9) Linearization
10) The Stable Manifold Theorem
11) The Hartman-Grobman Theorem
12) Stability and Liapunov Functions
13) Center Manifold Theorem
14) Gradient and Hamiltonian Systems

Sources

Course Notes / Textbooks: Differential Equations and Dynamical Systems, Lawrence Perko
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 3 % 10
Midterms 1 % 40
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 3 42
Homework Assignments 3 15 45
Midterms 1 30 30
Final 1 41 41
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To apply mathematical principles to real world problems.
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.