| Course Description |
|
| Course Name |
: |
Numerical Solution of Ordinary and Partial Differential Equations |
|
| Course Code |
: |
FK-603 |
|
| Course Type |
: |
Optional |
|
| Level of Course |
: |
Second Cycle |
|
| Year of Study |
: |
1 |
|
| Course Semester |
: |
Fall (16 Weeks) |
|
| ECTS |
: |
6 |
|
| Name of Lecturer(s) |
: |
Prof.Dr. METİN ÖZDEMİR
|
|
| Learning Outcomes of the Course |
: |
Knows the sources of some errors that results from numerical calculations and how to take precoutions
Knows the concepts of error, precision and stability
Knows how to classify differential equations. Knows the difference between an initial value problem a boundary value problem.
Knows numerical differantiaiton and how to apply it.
Knows how to solve initial value ordinary differential equations numerically. Applies it to various problems.
Knows how to plot the results obtained
Knows how to solve boundary value value ordinary and partial differential equations numerically. Knows how to apply to different problems.
Knows how to use these numerical methods in the solution of various problems in physics and other sciences
|
|
| Mode of Delivery |
: |
Face-to-Face |
|
| Prerequisites and Co-Prerequisites |
: |
None |
|
| Recommended Optional Programme Components |
: |
None |
|
| Aim(s) of Course |
: |
It is aimed to provide the basics of numerical computation; provide knowledge on how to solve ordinary and partial differential equations with initial or boundary value problems using complete sample program codes. The students are expected to have taken the basic courses of math and computer science. |
|
| Course Contents |
: |
Definition of machine precision, Finding the machine precision of the computers that are used, Solution of initial value ordinary differantial equations, Euler´s method, Runge Kutta Method, Solution of time independent Schrödinger equation for various potentials, Various applications, solution of heat equation, wave equation etc. |
|
| Language of Instruction |
: |
Turkish |
|
| Work Place |
: |
Lecture halls of faculty |
|
|
Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Error, precision and stability concepts. Definition of machine precision. |
Research the related topic |
Lecture, discussion and running program codes |
|
2 |
Simple inpu/output programs. Finding the machine precision of the computers that are used. |
Research the related topic |
Lecture, discussion and running program codes |
|
3 |
Numerical differantiation |
Research the related topic |
Lecture, discussion and running program codes |
|
4 |
Solution of initial value ordinary differantial equations, Euler´s method. |
Research the related topic |
Lecture, discussion and running program codes |
|
5 |
Euler-Richardson method, Runge-Kutta methods |
Research the related topic |
Lecture, discussion and running program codes |
|
6 |
Runge-Kutta methods (cont´d), numerical solution of various problems |
Research the related topic |
Lecture, discussion and running program codes |
|
7 |
Solution of boundary value ordinary differential equations. |
Research the related topic |
Lecture, discussion and running program codes |
|
8 |
Mid-term Exam |
Mid-term Exam |
Mid-term Exam |
|
9 |
Solution of time independent Schrödinger equation for various potentials. |
Research the related topic |
Lecture, discussion and running program codes |
|
10 |
Introduction to partial differential equations |
Research the related topic |
Lecture, discussion and running program codes |
|
11 |
Numerical solution of initial and boundary value partial differential equations. |
Research the related topic |
Lecture, discussion and running program codes |
|
12 |
Stability anaysis |
Research the related topic |
Lecture, discussion and running program codes |
|
13 |
Various applications, solution of heat equation, wave equation etc. |
Research the related topic |
Lecture, discussion and running program codes |
|
14 |
Term project |
Research the related topic |
Lecture, discussion and running program codes |
|
15 |
Term project |
Research the related topic |
Lecture, discussion and running program codes |
|
16/17 |
Final Exam |
Final Exam |
Final Exam |
|
|
| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Develop and deepen the knowledge as a specialist in physics or different areas based on the Physics Bachelor´s qualification level. |
3 |
|
2 |
Comprehend the importance of multidisciplinary studies related to Physics. |
4 |
|
3 |
Use his/her advanced theoretical and practical knowledge in Physics efficiently. |
4 |
|
4 |
Integrate and interpret the knowledge from different disciplines with the help of his professional knowledge in Physics and conceptualize new perspectives. |
2 |
|
5 |
Solve the problems in Physics by using research methods. |
3 |
|
6 |
Carry out a study requiring expertise in physics independently. |
4 |
|
7 |
Develop and provide new strategic approaches by taking responsibilty while solving the unexpected problems in Physics . |
4 |
|
8 |
Take the responsibility of being the leader while solving the problems related to physical environments. |
2 |
|
9 |
Evaluate the knowledge and skills gained in Physics by having a critical view and directs his/her learning. |
3 |
|
10 |
Systematically transfer the current developments in the field of physics and his/her work to the person in physics field or outside of the field by supporting qualitative and quantitative data. |
5 |
|
11 |
Take action to change the norms of social relations and critically examine these relationships, and develop them if necessary. |
4 |
|
12 |
Make communication in oral and written by using at least one foreign language in the level of European Language Portfolio B2 level. |
3 |
|
13 |
Use information and communication technologies in advanced level and use the software related with physics area.
|
4 |
|
14 |
Oversee social, scientific, cultural and ethical values in order to collect, implement, interpret data in Physics. |
4 |
|
15 |
Develop strategies, policies and implementation plans in the issues related to the field of physics and evaluate the results obtained within the framework of quality processes. |
2 |
|
16 |
Use the knowledge, problem solving, and / or practical skills obtained in the Physics Field in interdisciplinary studies. |
3 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
|
|