COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Vector Analysis * MT   236 4 2 2 4

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Assoc.Prof.Dr. Nazar Şahin ÖĞÜŞLÜ
Instructors
Doç.Dr.NAZAR ŞAHİN ÖĞÜŞLÜ1. Öğretim Grup:A
Doç.Dr.NAZAR ŞAHİN ÖĞÜŞLÜ2. Öğretim Grup:A
 
Assistants
Goals
Gain skills related to intangible and tangible aspects of vector analysis, to understand the basic concepts and physical applications of vector functions, line integrals, Green´s theorem and divergence theorem, teach understanding of abstract mathematical concept and abstract thinking.
Content
Vector functions, line integrals, Green´s theorem, surface integrals, divergence theorem

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
X
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Limit and derivative of vector functions. Review of the relevant pages from sources
2 Properties of the derivative of vector functions. Review of the relevant pages from sources
3 Motion along curve: speed, acceleration vector and uniform circular motion. Review of the relevant pages from sources
4 Tangential and normal compenents of the acceleration vector. Review of the relevant pages from sources
5 Newton and Kepler laws. Review of the relevant pages from sources
6 Vector and scalar fields and methods to obtain a new vector field from a vector field Review of the relevant pages from sources
7 Line integrals. Review of the relevant pages from sources
8 midterm exam Review of the topics discussed in the lecture notes and sources
9 Some physical applications of line integrals. (the work done along the curve, total flux) Review of the relevant pages from sources
10 Proof of Green´s theorem. Review of the relevant pages from sources
11 Green´s theorem for the regions bounded by two curves. Review of the relevant pages from sources
12 Conservative vector fields and fundemental theorem of line integrals. Review of the relevant pages from sources
13 Computation of surface integrals. Review of the relevant pages from sources
14 Proof of the Divergence theorem. Review of the relevant pages from sources
15 Some applications of divergence theorem Review of the relevant pages from sources
16-17 Final exam Review of the topics discussed in the lecture notes and sources

Recommended or Required Reading
TextbookCalculus and Analytic Geometry, Authors: Shermann K. Stein, Anthony Barcellos.
Additional Resources