COURSE SYLLABUS

VECTORAL ANALYSIS

1	Course Title:	VECTORAL ANALYSIS
2	Course Code:	MAT0538
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	0
6	Semester:	0
7	ECTS Credits Allocated:	4
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. AHMET TEKCAN
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	Uludağ Üniversitesi, Fen-Edebiyat Fakültesi Matematik Bölümü, 16059 Görükle Bursa-TÜRKİYE 0 224 294 17 51 tekcan@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim of the course is to make the students gain the some algebraic properties on vectorial analysis including, vector, line and plane in R^3, vector valued functions and theirs limits, derivatives and integrals, partial derivative, differential, tangent plane, linearization, Taylor series expansion, derivative with direction, gradient, arc integrals their applications, Green Theorem and its applications, surface integrals and their applications, Stokes and Divergens-Gauss theorems.
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	The course will be given as verbal exposition theoretically.;
2	Learn the definitions of vector, line, plane and some properties of it in R^3 also learn some properties of vector valued functions including limit, continuity, derivative and integral.;
3	Learn the partial derivatives, differential and chain rule, learn the derivatives with directions and gradient vector.;
4	Learn to calculate arc integrals and some theorems related to arc integrals and applications of Green theorem.;
5	Learn to calculate surface integrals and their application areas also Stokes and Divergens-Gauss theorems.;

22	Course Content:

Week	Theoretical	Practical
1	Overview of basic concepts on lessons
2	Some properties of vectors in R^3
3	Line, plane and some properties of them in R^3
4	Algebra of vector functions, limit and continuity of vector valued functions
5	Derivatives and integrals of vector valued functions and curvature
6	Partial derivatives
7	Differential, differentiable and their applications
8	Repeating courses and midterm exam
9	Tangent plane, linearization, chain rule and Taylor series expansion, derivative with direction, gradient vector and their applications
10	Arc integrals
11	Applications of arc integrals and some fundamental theorems on arc integrals
12	Green theorem and its applications
13	Surface integrals and their applications
14	Stokes and Divergence-Gauss theorems

23	Textbooks, References and/or Other Materials:	[1] A. Tekcan, Vektörel Analiz Ders Notları, 2009. [2] A. Tekcan. İleri Analiz. Dora Yayıncılık, 2009. [3] A.I. Khuri. Advanced Calculus with Applications in Statistics, 2003. [4] J. Stewart. Calculus. 5-th Edition, 2007. [5] A.E. Taylor ve W.R. Mann. Advanced Calculus. 3-th Edition, 1983. [6] S.R. Ghorpade ve B. V. Limaye. A Course in Multivariable Calculus and Analysis. Springer, 2010. [7] S. Lange. A First Course in Calculus Addision-Wesley P.C. London, 1980.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	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

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