BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| APPLIED MATHEMATICS (TURKISH, 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 | Spring | 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 |