| Course Type | Compulsory 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;
- An ability of numerical solution of ordinary and partial differential equations in the engineering problems
- An ability to apply knowledge of mathematics, science, and engineering
- An ability to identify, formulate, and solve engineering problems
- An ability to use the modern engineering techniques
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | None |
|---|
| Course Description | 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. |
|---|
| 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 |
Exam Week |
|
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. |
|
| Recommended or Required Reading | Erwin Kreyszig, Advanced Engineering Mathematics, 10th Ed.
Peter V. O Neil, Advanced Engineering Mathematics
|
|---|
| Planned Learning Activities and Teaching Methods |
- Questions/Answers
- Problem Solving
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
30 |
| Assignment |
5 |
30 |
| 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 |
|
|
|
| Individual or group work |
14 |
4 |
56 |
| Preparation for Final exam |
1 |
20 |
20 |
| Course hours |
14 |
3 |
42 |
| Preparation for Midterm exam |
1 |
20 |
20 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
5 |
30 |
150 |
| Take-home |
1 |
12 |
12 |
| Total Work Load | 304 |
| Total Work Load / 30 (h) | 10.13 |
| ECTS Credit of the Course | 10 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
