| 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;
- Numerically solve ordinary and partial differential equations encountered in engineering problems,
- Apply knowledge of engineering, science, and mathematics,
- Identify, formulate, and solve engineering problems,
- Use modern engineering techniques.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | None |
|---|
| Course Description | In this course, the concepts of Systems of linear equations; linear vector spaces, theory of matrices and the eigenvalue problem, multivariable differential calculus, ordinary differential equations, vectors in R3, vector field theory, Fourier series and Fourier transform, Laplace transform, calculus of variations are discussed. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Matrices, Operations on Matrices, Inverse Matrices |
|
2nd Week |
Determinants, Vectors |
|
3rd Week |
Gauss Elimination Method, Cramer?s Rule, Eigen Values, Eigen Vectors |
|
4th Week |
Similar Matrices, Diagonalization, Ordinary Differential Equations |
|
5th Week |
Ordinary Differential Equations |
|
6th Week |
Maclaurin and Taylor Series, Power Series Solutions of Ordinary Differential Equations |
|
7th Week |
Bessel?s Equation and Bessel?s Functions |
|
8th Week |
Midterm |
|
9th Week |
Integral Transformations; Laplace, Fourier, Hankel, Mellin Transformations |
|
10th Week |
Integral Transformations; Laplace, Fourier, Hankel, Mellin Transformations |
|
11th Week |
Fourier Series |
|
12th Week |
Complex Numbers, Complex Valued Functions, Analytic Functions, Cauchy-Riemann Equations |
|
13th Week |
An Introduction to Partial Differential Equations; The Method of Separation of Variables |
|
14th Week |
Variational Calculus, Optimization |
|
15th Week |
Course Review |
|
| Recommended or Required Reading | 1. Kreyszig, E. (2011). Advanced Engineering Mathematics (10th ed.), John Wiley & Sons.
2. O'Neil, P. V. (2006). Advanced Engineering Mathematics (6th ed.), Thomson Brooks/Cole. |
|---|
| 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 |
|---|
