| Course Type | Elective Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 5 |
|---|
| Name of Lecturer(s) |
|
| Learning Outcomes |
At the end of this course, the students;
- Understanding the principles of mathematical modeling and being able to develop appropriate mathematical models for physical systems.
- Being able to model engineering problems using ordinary and partial differential equations and apply numerical solution techniques.
- Being able to produce numerical solutions to engineering problems using finite differences, finite elements and finite volume methods.
- Being able to use software packages and simulation tools used in the mathematical modeling process effectively.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | It is suggested that students have previously taken courses on numerical analysis, differential equations, strength of materials, dynamics and heat transfer |
|---|
| Course Description | Aims and basic principles of mathematical modelling. Basic fields of interest: temperature, flow, pressure, velocity, stress, strain. Mathematical models for selected Mechanical Engineering problems selected from different areas of interest. Numerical solution techniques for differential equations. Software for mathematical modelling: pre-processors, solvers and post-processors |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Principles of mathematical modelling, nature of modelling and simulation. |
|
2nd Week |
Physical models, mathematical models, state variables, system parameters. |
|
3rd Week |
Classification of mathematical models, experimental data, simulation. |
|
4th Week |
Mechanistic models, ordinary differential equations (ODE). |
|
5th Week |
Numerical solution of ODE's. |
|
6th Week |
System of ODE's, numerical solution techniques. |
|
7th Week |
Basic concepts on numerical solutions of partial differential equations (PDE). |
|
8th Week |
Finite difference solution procedures |
|
9th Week |
Finite element solution procedures |
|
10th Week |
Finite volume solution procedures |
|
11th Week |
Numerical solution of heat equation. |
|
12th Week |
Numerical solution of structural mechanics problems |
|
13th Week |
Numerical solution of dynamic problems. |
|
14th Week |
Software for mathematical modelling: pre-processors, solvers and post-processors |
|
| Recommended or Required Reading | (1) Velten, K. Mathematical Modeling and Simulation: Introduction for Scientists and Engineers, Wiley-VCH (2) Basmadjian, D. Mathematical Modeling of Physical Systems: An Introduction. Oxford University Press |
|---|
| Planned Learning Activities and Teaching Methods |
- Presentation
- Lecture
- Other
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Assignment |
1 |
15 |
| Attendance |
1 |
5 |
| 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 |
3 |
2 |
6 |
| Individual or group work |
14 |
3 |
42 |
| Preparation for Final exam |
14 |
1.5 |
21 |
| Course hours |
14 |
3 |
42 |
| Preparation for Midterm exam |
7 |
1.5 |
10.5 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
3 |
3 |
| Homework |
2 |
3 |
6 |
| Quiz |
3 |
1 |
3 |
| Total Work Load | 135.5 |
| Total Work Load / 30 (h) | 4.51 |
| ECTS Credit of the Course | 5 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
