| Course Name | Code | Semester | T+U Hours | Credit | ECTS |
|---|---|---|---|---|---|
| Nonlinear Partial Differantial Equations | MAT 623 | 0 | 3 + 0 | 3 | 6 |
| Precondition Courses | <p>Recommended course of undergraduate education has received partial differential equations.</p> |
| Recommended Optional Courses | |
| Course Language | Turkish |
| Course Level | Doctorate Degree |
| Course Type | Optional |
| Course Coordinator | Prof.Dr. ÖMER FARUK GÖZÜKIZIL |
| Course Lecturers | |
| Course Assistants | |
| Course Category | |
| Course Objective | It is useful for graduate students in mathematics and engeneering. |
| Course Content | Adomian Decomposition Method , Solution of Nonlinear PDEs by Adomian Method, Solution of Nonlinear PDEs Systems by Adomian Method. Linear and Nonlinear Physical Models. The Goursat Problem. The Telegraph Equation .Schrodinger Equation. Fourth-order Parabolic Equation. The Pad´e Approximants. Solitons and Compactons. |
| # | Course Learning Outcomes | Teaching Methods | Assessment Methods |
|---|---|---|---|
| 1 | To learn the details of partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | To recognize the non-linear partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 3 | To learn methods of solution of nonlinear partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 4 | To learn the methods of numerical solution of nonlinear partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 5 | To learn to linear and nonlinear physical models. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 6 | To solve to the Goursat problem, telegraph equation and the Schrodinger equation. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| Week | Course Topics | Preliminary Preparation |
|---|---|---|
| 1 | Adomian decomposition method. | |
| 2 | Solution of nonlinear partial differential equations by using adomian method. | |
| 3 | Solution of nonlinear partial differential equations by using adomian method. | |
| 4 | Linear and Nonlinear Physical Models. | |
| 5 | The Goursat Problem. | |
| 6 | The Telegraph Equation. | |
| 7 | Schrodinger Equation. | |
| 8 | Fourth-order Parabolic Equation. | |
| 9 | Midterm | |
| 10 | The Pad´e Approximants. | |
| 11 | The Pad´e Approximants. | |
| 12 | Solitons | |
| 13 | Solitons | |
| 14 | Compactons |
| Resources | |
|---|---|
| Course Notes | |
| Course Resources | 1.Nonlinear Partial Differential Equations for Scientist and Engineers,Debnath L., Boston , 1997. |
| Order | Program Outcomes | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
| 1 | At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. | X | |||||
| 2 | Student completes the missing or limited knowledge by using the scientific methods. | X | |||||
| 3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | X | |||||
| 4 | Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. | X | |||||
| 5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | X | |||||
| 6 | At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. | X | |||||
| 7 | Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. | X | |||||
| 8 | Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. | X | |||||
| 9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | X | |||||
| 10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | X | |||||
| 11 | Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. | X | |||||
| Evaluation System | |
|---|---|
| Semester Studies | Contribution Rate |
| 1. Ara Sınav | 60 |
| 1. Kısa Sınav | 20 |
| 1. Ödev | 20 |
| Total | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Total | 100 |
| ECTS - Workload Activity | Quantity | Time (Hours) | Total Workload (Hours) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 20 | 20 |
| Quiz | 1 | 10 | 10 |
| Assignment | 1 | 10 | 10 |
| Final examination | 1 | 15 | 15 |
| Total Workload | 151 | ||
| Total Workload / 25 (Hours) | 6.04 | ||
| dersAKTSKredisi | 6 | ||