COURSE SYLLABUS

REEL ANALYSIS I

1	Course Title:	REEL ANALYSIS I
2	Course Code:	MAT5101
3	Type of Course:	Compulsory
4	Level of Course:	Second Cycle
5	Year of Study:	1
6	Semester:	1
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	none
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. OSMAN BİZİM
16	Course Lecturers:	Prof. Dr. Osman Bizim
17	Contactinformation of the Course Coordinator:	Uludağ Üniversitesi, Fen-Edebiyat Fakültesi Matematik Bölümü, Görükle Bursa-TÜRKİYE 0 224 294 17 57 / obizim@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim of this course is to review student’s undergradute analysis courses and to correct the deficiencies. So students can be su have succsessful in graduate studies.
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	Learns the real number system, Euclidean Spaces, metric spaces, basic topological properties of R.;
2	Learns compact and connected sets and their properties, sequences and series.;
3	Learns power series, absolute convergence.;
4	Learns countinuity and continous functions and their properties;
5	Learns differentiation and properties of the differentiable functions.;
6	Learns The Riemann-Stieltjes integral and its properties.;
7	Learns sequences and series of functions and their properties, uniform convergence,;

22	Course Content:

Week	Theoretical	Practical
1	The real and complex number system, Euclidean Spaces, metric spaces and their properties
2	Basic topological properties of R, compact and connected sets and their properties
3	Sequences and series in R and C, and their properties
4	Power series and absolute convergence, addition and multiplicatio of series
5	Countinuity and continous functions and their properties
6	Differentiation and properties of the differentiable functions
7	Mean value theorem and its applications
8	Vector-valued functions and their properties
9	The Riemann-Stieltjes integral and its properties
10	Integration of vector-valued functions
11	Sequences and series of functions and their properties, uniform convergence, The Stone-Weierstrass theorem, some special functions.
12	Uniform convergence of sequences and series of functions
13	The Stone-Weierstrass theorem and its applications
14	Some special functions, the exponential and the logarithmic functions, the trigonometric functions, Fourier series, the Gamma function and their properties

23	Textbooks, References and/or Other Materials:	[1] Principles of Mathematical Analysis, W. Rudin, [2] Real and Complex Analysis, W. Rudin, [3] Real Analysis, H. L. Royden, [4] Introduction to Real Analysis, W. F. Trench.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	0	0
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	100
Total	1	100
Contribution of Term (Year) Learning Activities to Success Grade		0
Contribution of Final Exam to Success Grade		100
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High