1	Course Title:	ANALYSIS IV
2	Course Code:	MAT2002
3	Type of Course:	Compulsory
4	Level of Course:	First Cycle
5	Year of Study:	2
6	Semester:	4
7	ECTS Credits Allocated:	10
8	Theoretical (hour/week):	4
9	Practice (hour/week) :	2
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:	Dr. Ögr. Üyesi ELİF YAŞAR
16	Course Lecturers:	Analiz ve Fonksiyonlar Teorisi bilim dalı öğretim üyeleri
17	Contactinformation of the Course Coordinator:	elifyasar@uludag.edu.tr, 0(224) 2942872, U.Ü. Fen-Ed. Fak. Matematik Bölümü, Görükle/BURSA.
18	Website:
19	Objective of the Course:	to learn definitions, properties and calculations of multiple, line and surface integrals in Euclidean spaces.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Definition and calculation of double integrals.; 2 Change of variables and polar coordinates in double integrals; 3 Calculation of double improrer integrals ; 4 Definition and calculation of triple integrals.; 5 Calculations of triple integrals in cylindrical and spherical coordinates ; 6 Line integrals of scalar and vector functions; 7 Definitions of independence of path and gradien and planar Green and Divergence theorems; 8 Surface integrals, Divergence and Stokes Theorems.;

22	Course Content:

Week	Theoretical	Practical
1	Definition and calculation of double integrals.	Solutions of exercises of related subject
2	Change of variables and polar coordinates in double integrals.	Solutions of exercises of related subject
3	Improrer double integrals.	Solutions of exercises of related subject
4	Definition and calculation of triple integrals.	Solutions of exercises of related subject
5	Triple integrals in cylindrical and spherical coordinates.	Solutions of exercises of related subject
6	Line integrals of scalar functions.	Solutions of exercises of related subject
7	Line integrals of vector functions.	Solutions of exercises of related subject
8	Definitions of independence of path and gradien	Solutions of exercises of related subject
9	Planar Green theorem and Divergence theorem	Solutions of exercises of related subject
10	Definitions of surface, tangent plane and normal .	Solutions of exercises of related subject
11	Area of Surface.	Solutions of exercises of related subject
12	Surface integrals.	Solutions of exercises of related subject
13	Dievergence and Stokes Theorems	Solutions of exercises of related subject
14	Summary	Solutions of exercises of related subject

23	Textbooks, References and/or Other Materials:	M., BAYRAKTAR, Analiz, Nobel Yay. 2010. B. MUSAYEV, K. KOCA, N. MUSTAFAYEV, Analiz IV, Seçkin Yayınevi 2006. M. BALCI, Matematik Analiz II, Balcı Yayınları, 2005. J.E.MARSDEN, A.J.TROMBA, Vector Calculus, Freeman company, 2003. S. LANG, Calculus of Several Variables, 3rd ed., Springer-Verlag, New York, 1987.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	2	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	3	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
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	4	56
Practicals/Labs	14	2	28
Self Study and Preparation	14	10	140
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	2	15	30
Others	2	15	30
Final Exams	1	15	15
Total WorkLoad			299
Total workload/ 30 hr			9,97
ECTS Credit of the Course			10

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 2 4 1 3 4 1 1 4 4 1 LO2 1 4 1 3 4 1 4 4 3 1 LO3 1 3 1 3 4 1 1 4 3 1 LO4 1 4 1 3 4 1 2 4 3 0 LO5 1 4 1 3 4 2 1 4 3 1 LO6 1 4 1 3 4 1 1 4 3 1 LO7 1 4 1 3 4 1 2 4 3 0 LO8 1 4 1 3 4 1 1 4 3 1

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High