| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4065 | Partial Differential Equations II | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Dr. Öğr. Üyesi TUĞCAN DEMİR |
| Course Objectives: | 1. Find the Green’s function of a PDE using Fourier methods. 2. Transform a PDE into an integral equation. 3. Determine the existence and uniqueness of solutions of PDEs and integral equations. 4. Determine the salient features of the spectrum of PDEs and integral equations. |
|
The students who have succeeded in this course; Explain the basic concepts of Partial Differential Equations. Obtain and Explain the Fundamental Definitions, Concepts, Theorems and Applications of Partial Differential Equations. Gain Experience on Partial Differential Equations. Generalize, Emphasize and Apply the concept of Theory of Ordinary Differential Equations to the Partial Differential Equations. Explain and Apply the principles of Theory of Ordinary Differential Equations to the Partial Differential Equations. Interpret the Stability results and Applications of Partial Differential Equations. Distinguish the difference between Partial Differential Equations and Fractional order Partial Differential Equations. Develop awareness for the Partial Differential Equations. |
| Week 1: Classification and characteristics of PDEs; Week 2: Transform method,Green’s function methods; Week 3: Eliptic problems; Week 4: Parabolic problems; Week 5: Hyperbolic problems; Week 6: Nonvariational techniques; Week 7: Hamilton-Jacobi equation; Week 8: Systems of conservation laws and shocks; Week 9: MIDTERM Week 10: Fourier Transform; Week 11: Laplace Transform Week 12: Weak derivatives; Week 13: Sobolev Spaces; Week 14: Sobolev Inequalities; Week 15: General review Week 16: Final |
| Week | Subject | Related Preparation | |
| 1) | Classification and characteristics of PDEs; | ||
| 1) | Review | ||
| 2) | Transform method,Green’s function methods; | ||
| 3) | Eliptic problems; | ||
| 4) | Parabolic problems; | ||
| 5) | Hyperbolic problems; | ||
| 6) | Nonvariational techniques; | ||
| 7) | Hamilton-Jacobi equation; | ||
| 8) | Systems of conservation laws and shocks; | ||
| 10) | Fourier Transform; | ||
| 11) | Laplace Dönüşümü | ||
| 12) | Weak derivatives; | ||
| 13) | Sobolev Spaces; | ||
| 14) | Sobolev Inequalities; | ||
| Course Notes: | |
| References: | 1. Partial Differential Equations: An Introduction / W. A. Strauss. 2. An Introduction to Partial Differential Equations / Y. Pinchover and J. Rubinstein. 3. Partial Differential Equations of Mathematical Physics and Integral Equations / R. B. Guenther and J. W. Lee. 4. Partial Differential Equations / L. C. Evans. |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 3 | % 10 |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 3 | 10 | 30 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 10 | 10 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 15 | 15 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |