sylvain.lavau@gmail.com
Content
Objective
The course aims to offer a new understanding of real analysis seen at undergraduate level, but in a more topological perspective. We try to understand what is the norm in analysis, and what is the exception. We don't prove everything but will try to get a deeper understanding and hope to consolidate your understanding in Real Analysis.
Course Content
1. Basic facts of real analysis, normed vector spaces, metric topology
2. Banach spaces
3. Banach spaces 2
4. Baire Theory
5. Nowhere continuous/differentiable functions and Darboux functions
6. Baire 1 functions and set of discontinuities of real functions
7. Set of convergence of sequences of functions and power series
8. Mid-term exam
9. Integration of functions in |R^2
10. Parametrized curves and Green Theorem
11. Parametrized surfaces and Stokes Theorem
12. Holomorphic functions and Cauchy theory
13. Laurent series, singularities and residues
14. Conformal applications
Weekly Contents
| Week | Weekly Contents |
|---|---|
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| 8 | Ara Sınav |
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| 14 |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 50 |
| Contribution of final exam to overall grade | 1 | 50 |
| Total | 3 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 2 | 15 |
| Presentation | 1 | 5 |
| Midterm Examinations (including preparation) | 1 | 30 |
| 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 | 4 | 50 |
Relation of Proficiency
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
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| 12 | X | |||||
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| 15 | X | |||||
| 16 | X | |||||
| 17 | X | |||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 15 | 5 | 75 |
| Final Examinations (including preparation) | 1 | 71 | 71 |
| Total Workload | 188 | ||
| Total Workload / 25 | 7.52 | ||
| Credits ECTS | 8 | ||