Partial Differential Equations(MAT328)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT328 | Partial Differential Equations | 6 | 4 | 0 | 0 | 4 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | SUSUMU TANABE tanabesusumu@hotmail.com (Email) |
| Assistant | |
| Objective | Introduction to Fourier analysis, to theory of linear PDE. |
| Content | Fourier series, Separation of variables, Heat equation, Wave equation. Laplace equation, harmonic functions. |
| Course Learning Outcomes |
1. Learn fundamental theorems on the Fourier series e.g. Parseval formula. 2. Make acquaintance with several applications of Fourier analysis to PDE. 3. Understand the fundamental properties of heat, wave, elliptic equations. 4. Get ideas on three types of PDE =hyperbolic, parabolic, elliptic. |
| Teaching and Learning Methods | Lectures and exercises. |
| References |
Equations aux dérivées partielles, Introduction. H.Reinhard, Dunod, 1991. Analyse 2, Calcul différentiel, intégrales multiples, séries de Fourier. F.Cottet-Emard, De Boeck, 2006 |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Fourier series |
| 2 | Fourier series |
| 3 | Dirichlet's theorem |
| 4 | Bessel inequality, Parseval formula. |
| 5 | Heat equation |
| 6 | Mid term examination. |
| 7 | Separation of variables |
| 8 | Wave equation |
| 9 | Wave equation |
| 10 | Initial value problem for the heat equation. |
| 11 | Laplace equation |
| 12 | Harmonic functions |
| 13 | Boundary value problems |
| 14 | Green's function |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 7 | 61 |
| Contribution of final exam to overall grade | -1 | 40 |
| Toplam | 6 | 101 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 60 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 2 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 14 | 4 | 56 |
| Presentation | 2 | 1 | 2 |
| Midterm Examinations (including preparation) | 2 | 30 | 60 |
| Final Examinations (including preparation) | 1 | 20 | 20 |
| Total Workload | 194 | ||
| Total Workload / 25 | 7,76 | ||
| Credits ECTS | 8 | ||