(MATH 501) | GSÜ - ECTS Information Guide

Content

Objective

The course aims to cover some parts of the content of Mat 101,102, 201, 202, 301,331 and 452 given in the undergraduate level at Galatasaray University. We try to understand definitions, theorems, and proofs of some results in Real Analysis. 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. Sequences and limits in normed vector spaces, uniform convergence
3. Cauchy sequences and Banach spaces
4. Series of vectors and functions, and their convergence properties
5. Continuity in normed vector spaces, differentiability in |R^n
6. Gradient vector field and implicit function theorem
7. Extrema and Hessian, Taylor expansion
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

References

1) A. W. Knapp, Basic Real Analysis, with an appendix ”Ele- mentary Complex Analysis”, Digital Second Edition, 2016.
2) G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 1999.
3) W. Rudin, Real and Complex Analysis, McGraw-Hill Inc., 1966.

Weekly Contents

Theory Topics
Week	Weekly Contents
1
2
3
4
5
6
7
8	Ara Sınav
9
10
11
12
13
14

Assessment System

Contribution to Overall Grade
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

In-Term Studies
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
No	Program Learning Outcomes	1	2	3	4	5
1						X
2						X
3		X
4						X
5						X
6				X
7					X
8						X
9					X
10				X
11						X
12				X
13				X
14				X
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