Rapor Tarihi: 13.04.2026 03:09
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Differential Equations II | MAT232 | Turkish | Compulsory | 4. Semester | 2 + 2 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Prof. Dr. İlhame AMİRALİ |
| Instructor(s) | Prof. Dr. İlhame AMİRALİ (Bahar) |
| Goals | To give advance concepts of ordinary differantial equations. |
| Course Content | Second order linear equations with variable coefficients and non-linear differential equations; Euler equations; Power series solutions about an ordinary points and singular points; Legendre ve Bessel equations, Laplace and Inverse Laplace transformations and their properties; Solving linear differential equations with constant variables using the Laplace transform. |
| # | Öğrenme Kazanımı |
| 1 | To know solution methods of higher order differential equations To solve a given higher order differential equation by using suitable solution method. |
| 2 | Ability to understand the applications of the Cauchy–Euler equation |
| 3 | Comprehension of the types of linear systems of equations, the operator method for constant-coefficient linear systems, and their application |
| 4 | Ability to understand linear systems in normal form, as well as homogeneous and non-homogeneous linear systems |
| 5 | Analysis of constant-coefficient homogeneous linear systems based on the nature of their characteristic roots |
| 6 | Comprehension and application of Sturm–Liouville problems, including eigenvalues and eigenfunctions |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Second order linear and nonlinear differential equations with variable coefficient | |
| 2. Week | Euler Equation | |
| 3. Week | Power series solutions about an ordinary points | |
| 4. Week | Power series solutions about a singular point | |
| 5. Week | Power series solutions about a singular point | |
| 6. Week | Legendre and Bessel Equations | |
| 7. Week | Legendre and Bessel Equations | |
| 8. Week | Laplace transformation and its properties; Inverse Laplace Transformation | |
| 9. Week | Laplace transformation and its properties; Inverse Laplace Transformation | |
| 10. Week | Laplace transformation and its properties; Inverse Laplace Transformation | |
| 11. Week | Convolution and the function of order with united | |
| 12. Week | Solution of constant coefficient linear differential equations by Laplace transform | |
| 13. Week | Solution of constant coefficient linear differential equations by Laplace transform | |
| 14. Week | Solution of constant coefficient linear differential equations by Laplace transform |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 |
|---|---|---|---|---|---|---|
| PY1 | 5 | 0 | 0 | 0 | 0 | 0 |
| PY2 | 5 | 0 | 0 | 0 | 0 | 0 |
| PY3 | 3 | 0 | 0 | 0 | 0 | 0 |
| PY4 | 2 | 0 | 0 | 0 | 0 | 0 |
| PY5 | 1 | 0 | 0 | 0 | 0 | 0 |
| PY6 | 1 | 0 | 0 | 0 | 0 | 0 |
| PY7 | 5 | 0 | 0 | 0 | 0 | 0 |
| PY8 | 2 | 0 | 0 | 0 | 0 | 0 |
| PY9 | 2 | 0 | 0 | 0 | 0 | 0 |
| PY10 | 5 | 0 | 0 | 0 | 0 | 0 |
| PY11 | 4 | 0 | 0 | 0 | 0 | 0 |
| PY12 | 4 | 0 | 0 | 0 | 0 | 0 |
| PY13 | 5 | 0 | 0 | 0 | 0 | 0 |
| PY14 | 2 | 0 | 0 | 0 | 0 | 0 |
| PY15 | 1 | 0 | 0 | 0 | 0 | 0 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| Bahar Dönemi | |||
| Responsible Personnel | Grup | Evaluation Method | Percentage |
|---|---|---|---|
| Prof. Dr. İlhame AMİRALİ | Vize | 40.00 | |
| Prof. Dr. İlhame AMİRALİ | Final | 60.00 | |
| Toplam | 100.00 | ||
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 4 | 56 |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Homework | 14 | 1 | 14 | |
| Homework Preparation | 14 | 1 | 14 | |
| Final | 1 | 2 | 2 | |
| Practice | 14 | 1 | 14 | |
| Classroom Activities | 14 | 2 | 28 | |
| Total Workload | 130 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
