| Course Type | Elective Course |
|---|
| Course Level | Master's Degree With Thesis |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 10 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- Classify differential equations and determine appropriate solution methods,
- Solve first-order differential equations including separable, homogeneous, exact, linear, and Bernoulli equations,
- Apply analytical techniques such as Laplace transforms, power series, and variation of parameters to solve differential equations,
- Formulate and solve systems of differential equations and interpret their applications in engineering and scientific problems.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | None |
|---|
| Course Description | This course covers the origin, classification and solution methods of differential equations. Topics include isoclines, equations separable in variables, homogeneous equations, exact differential equations, linear differential equations, Bernoulli's equation, higher order equations, equations with constant coefficients, equations with variable coefficients, Cauchy's equation, Legendre's equation, variation of parameters, power series solution, Laplace transforms, systems of differential equations and partial differential equations. This course aims to provide the basic knowledge and skills necessary to understand and apply numerical solutions of differential equations. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Introduction to Differential Equations and Classification |
|
2nd Week |
Isoclines and Separable Equations |
|
3rd Week |
Homogeneous Equations |
|
4th Week |
Exact Differential Equations |
|
5th Week |
First-Order Linear Equations and Bernoulli Equations |
|
6th Week |
Higher-Order Differential Equations |
|
7th Week |
Linear Equations with Constant Coefficients |
|
8th Week |
Midterm |
|
9th Week |
Variable Coefficient Equations |
|
10th Week |
Cauchy and Legendre Equations |
|
11th Week |
Variation of Parameters Method |
|
12th Week |
Power Series Solutions |
|
13th Week |
Laplace Transforms and Applications |
|
14th Week |
Systems of Differential Equations |
|
15th Week |
Partial Differential Equations and Numerical Methods |
|
| Recommended or Required Reading | 1. Rainville, E.D., Bedient P.E.,Bedient R.E., Elementary Differential Equations (1997), Prentice Hall.
2. Shepley L. Ross, Differential Equations (1984), John Wiley&Sons. |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
- Presentation
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
30 |
| Assignment |
1 |
10 |
| Quiz |
1 |
20 |
| Total(%) |
|
60 |
| Contribution of In-term Studies to Overall Grade(%) |
|
60 |
| Contribution of Final Examination to Overall Grade(%) |
|
40 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
1 |
50 |
50 |
| Individual or group work |
14 |
3 |
42 |
| Preparation for Final exam |
1 |
80 |
80 |
| Course hours |
14 |
3 |
42 |
| Preparation for Midterm exam |
1 |
60 |
60 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
1 |
20 |
20 |
| Quiz |
1 |
2 |
2 |
| Total Work Load | 300 |
| Total Work Load / 30 (h) | 10 |
| ECTS Credit of the Course | 10 |
|
| Language of Instruction | English |
|---|
| Work Placement(s) | No |
|---|
