APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5011 | Differential Equations I | Fall Spring |
3 | 0 | 3 | 12 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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 |
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 |
Linear Systems, Stability Thoery, The Fundamental Existence and Uniqueness Theorem, Local Theory of Dynamical Systems, The Stable Manifold Theorem, The Hartman-Grobman Theorem |
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 |
Course Notes / Textbooks: | Differential Equations and Dynamical Systems, Lawrence Perko |
References: |
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 |
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 |
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. | 5 |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | 4 |
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 |
4) | Ability to make individual and team work on issues related to working and social life. | 4 |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | 5 |
6) | Ability to use mathematical knowledge in technology. | 5 |
7) | To apply mathematical principles to real world problems. | 5 |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | 4 |
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. | 5 |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | 4 |
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. | 4 |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, | 5 |