1	Course Title:	ADVANCED ANALYSIS II
2	Course Code:	MAT5108
3	Type of Course:	Optional
4	Level of Course:	Third Cycle
5	Year of Study:	1
6	Semester:	2
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	No
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Dr. Ögr. Üyesi ELİF YAŞAR
16	Course Lecturers:	Prof.Dr. Metin ÖZTÜRK
17	Contactinformation of the Course Coordinator:	syalcin@uludag.edu.tr, 0(224)2941758, U.Ü. Fen Edebiyat Fakültesi Matematik Bölümü, 16059 BURSA
18	Website:
19	Objective of the Course:	To make the students to get the necessary knowledges about the Mathematical Analysis they they would need in the rlated branches on the General Mathematics knowledges.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 He/she determines the characters of the series with positive terms.; 2 He/she determines the characters of the alterne series.; 3 He/she determines the characters of the series with arbitrary terms.; 4 He/she researches if the functions series are convergent and uniform; 5 He/she calculates the derivative and integral of the power series.; 6 He/she finds the küme that is convergent of the power series.; 7 He/she calculates Taylor’s series expansion of a function.; 8 He/she calculates the infinite multiplications.; 9 He/she uses the Gamma and Beta functions.; 10 He/she knows the application areas of the fourier series.;

22	Course Content:

Week	Theoretical	Practical
1	The series with positive terms and The convergence criterions fort he series with positive term
2	The Alterne series and The Leibntiz criterions for Alterne series
3	The series with arbitrary terms and the convergence criterions for these series
4	The relations uniformly convergent series and limit, integral and derivative
5	The uniformly convergent of the function series.
6	The power series, the derivatives and integral of the power series.
7	The Taylor’s polynoms and Taylor series.
8	The infinite multiplications.
9	The convergence criterions for the generalized integrals and generalized integrals.
10	Gamma and Beta Functions
11	The Fourier series.
12	The application areas of the Fourier series.
13	The Fejer Theorem, and the theorems of convergence
14	Orthogonal functions

23	Textbooks, References and/or Other Materials:	Principles of Mathematical Analysis, W. Rudin,
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	0	0
Quiz	0	0
Homeworks, Performances	1	50
Final Exam	1	50
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		50
Contribution of Final Exam to Success Grade		50
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	8	112
Homeworks, Performances	1	43	43
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	0	0	0
Others	0	0	0
Final Exams	1	28	28
Total WorkLoad			225
Total workload/ 30 hr			7,5
ECTS Credit of the Course			7,5

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 5 5 1 1 2 3 4 4 4 2 LO2 5 5 1 1 2 3 4 4 4 2 LO3 5 5 1 1 2 3 4 4 4 2 LO4 5 5 1 1 2 3 4 4 4 2 LO5 5 5 1 1 2 3 4 4 4 2 LO6 5 5 1 1 2 3 4 4 4 2 LO7 5 5 1 1 2 3 4 4 4 2 LO8 5 5 1 1 2 3 4 4 4 2 LO9 5 5 1 1 2 3 4 4 4 2 LO10 5 5 1 1 2 3 4 4 4 2

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High