Single Variable Analysis I(MAT101)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT101 | Single Variable Analysis I | 1 | 3 | 2 | 0 | 5 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Begüm Gülşah ÇAKTI (Email) Sylvain LAVAU sylvain.lavau@gmail.com (Email) |
| Assistant | |
| Objective | To build, with appropriate rigour, the foundations of calculus and along the way to develop the skills to enable us to continue studying mathematics |
| Content | Course syllabus : Real Numbers, Sequences, Topology of R, Continuity, Limits |
| Course Learning Outcomes | The student is expected to learn the main notions ( Real Numbers, Sequences, Topology of R, Continuity, Limits). |
| Teaching and Learning Methods | Course and the problem solving |
| References |
- Analyse 1re année : Cours et exercices avec solution Liret, François, Dominique Martinais - Maths en pratique - 1re édition - A l'usage des étudiants Liret, Françoise - First Course in Real Analysis, Sterling K.Berberian, Springer - Mathématiques : tout-en-un : 1re année : cours et exercices corrigés : MPSI-PCSI Mathématiques : tout-en-un : 1re année : cours et exercices corrigés : MPSI-PCSI |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Set, maps and the language |
| 2 | Real Numbers |
| 3 | Real Numbers |
| 4 | Midterm 1 |
| 5 | Sequences |
| 6 | Sequences |
| 7 | LImits and Continuity |
| 8 | Limits and Continuity |
| 9 | Limits and Continuity |
| 10 | Midterm 2 |
| 11 | Derivation |
| 12 | Derivation |
| 13 | Parametric Curves |
| 14 | Parametric Curves |
Practice Topics
| Week | Weekly Contents |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
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| 14 |
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 4 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 45 |
| 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 | 1 | 15 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 3 | 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 | 5 | 70 |
| Working Hours out of Class | 14 | 3 | 42 |
| Assignments | 2 | 3 | 6 |
| Presentation | 4 | 6 | 24 |
| Midterm Examinations (including preparation) | 2 | 12 | 24 |
| Final Examinations (including preparation) | 1 | 15 | 15 |
| Term Paper/ Project | 1 | 3 | 3 |
| Total Workload | 184 | ||
| Total Workload / 25 | 7.36 | ||
| Credits ECTS | 7 | ||