| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6017 | Differential Equations II | Fall | 3 | 0 | 3 | 8 |
| 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: | Bu ders doğrusal olmayan sistemleri veya adi diferansiyel denklemlerin çalışmasına ayrılmıştır.Birincil amaç, değişmez setler dahil olmak üzere ve diferansiyel denklemler sistemi tarafından tanımlanan dinamik sistem veya akış davranışını sınırlayan diferansiyel denklemlerin bir sistemin niteliksel davranışını tanımlamaktır. |
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The students who have succeeded in this course; 1. To learn and solve the nonlinear systems 2. To learn the fundamental Existence and Uniqueness theorem 3. To learn the local theory of dynamical systems |
| Nonlinear Systems: Lokal Theory, Fundamental existence theorem, dependence on initial conditions and parameters, the maximal interval of existence, Flow defined by a differential equation. Linearization, stable manifold theorem, Hartman-Grobman theorem, Stability and Liapunov functions, Saddles, Nodes, Foci and centers, Nonhyperbolic critical points in R^2, Center Manifold and Normal form Theory, Gradient and Hamiltonian system. |
| Week | Subject | Related Preparation |
| 1) | Nonlinear systems: Basic definiitons and concepts. | |
| 2) | The Fundamental Existence-Uniqueness Theorem | |
| 3) | Dependence on Initial Conditions and Parameters | |
| 4) | The Maximal Interval of Existence | |
| 5) | The Flow Defined by a Differential Equation | |
| 6) | Linearization | |
| 7) | The Stable Manifold Theorem | |
| 8) | The Hartman-Grobman Theorem | |
| 10) | Stability and Liapunov Functions | |
| 11) | Saddles, Nodes, Foci and Centers | |
| 12) | Nonhyperbolic Critical Points | |
| 13) | Center Manifold and Normal form Theory | |
| 14) | Gradient and Hamiltonian Systems. |
| Course Notes / Textbooks: | Differential Equations and Dynamical Systems, Lawrence Perko |
| References: | Ordinary Differential Equations,Jack K. Hale Hirsch and Smale – Differential Equations, Dynamical Systems, and Liner Algebra - Academic Press, New York, (1974) |
| 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 | 3 | 20 | 60 |
| Homework Assignments | 3 | 15 | 45 |
| Midterms | 1 | 23 | 23 |
| Final | 1 | 30 | 30 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |