Differential Equations
aouzeri@gsu.edu.tr
Content
Objective
To master: Existence and uniqueness of the solution to ordinary differential equation, Lipschitz condition, second-order linear differential equation, linear system of first-order differential equations.
Course Content
Existence and uniqueness of the solution to ordinary differential equation, Lipschitz condition, second-order linear differential equation, linear system of first-order differential equations.
Course Learning Outcomes
To understand: Existence and uniqueness of the solution to ordinary differential equation, Lipschitz condition, second-order linear differential equation, linear system of first-order differential equations.
Teaching and Learning Methods
Course and exercises
References
Equations différentielles ordinaires, Etudes qualitatives, Dominique Hulin, Notes de Cours à L'université Paris Sud.
Cours de mathématiques, tome 4 : Équations différentielles, intégrales multiples - Cours et exercices corrigés, Jacqueline Lelong-Ferrand et Jean-Marie Arnaudiès, Dunod.
Calcul différentiel et équations différentielles - Sylvie Benzoni-Gavage
Mathématiques tout-en-un pour la licence 2 - Halberstadt, Ramis, Sauloy, Buff, Moulin
Équations différentielles ordinaires - Millot
Équations différentielles ordinaires - Gallouet
Weekly Contents
| Week | Weekly Contents |
|---|---|
| 1 | Gneralities and first definitions |
| 2 | Linear differential equations |
| 3 | Linear differential equations with constant coefficients |
| 4 | Phase portrait |
| 5 | Midterm 1 |
| 6 | Cauchy-Lipschitz theorem |
| 7 | Grönwall's inequality |
| 8 | Autonomous vector fields |
| 9 | Regular and stationary points |
| 10 | midterm 2 |
| 11 | Lyapunov stability |
| 12 | Bifurcations |
| 13 | Solution operator |
| 14 | Wronskian |
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Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 4 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Total | 5 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 10 | 5 |
| Presentation | 1 | 5 |
| Midterm Examinations (including preparation) | 2 | 50 |
| 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 |
| Total | 13 | 60 |
Relation of Proficiency
| 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; | |||||
| 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 | ||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 14 | 6 | 84 |
| Midterm Examinations (including preparation) | 2 | 15 | 30 |
| Total Workload | 170 | ||
| Total Workload / 25 | 6.80 | ||
| Credits ECTS | 7 | ||