MT236 Vector Analysis

4 ECTS - 2-0 Duration (T+A)- 4. Semester- 2 National Credit

Information

Code MT236
Name Vector Analysis
Semester 4. Semester
Duration (T+A) 2-0 (T-A) (17 Week)
ECTS 4 ECTS
National Credit 2 National Credit
Teaching Language Türkçe
Level Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ


Course Goal

Gain skills related to intangible and tangible aspects of vector analysis, to understand the basic concepts and physical applications of vector functions, line integrals, Greens theorem and divergence theorem, teach understanding of abstract mathematical concept and abstract thinking.

Course Content

Vector functions, line integrals, Greens theorem, surface integrals, divergence theorem

Course Precondition

No

Resources

Calculus and Analytic Geometry, Authors:Shermann K. Stein, Anthony Barcellos.

Notes

Calculus and Analytic Geometry, Authors: Shermann K. Stein, Anthony Barcellos.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Prove the properties of vector functions using their basic concepts.
LO02 Uses basic properties of vector functions to solve some problems of physics.
LO03 Calculates line integrals.
LO04 Prove the basic properties of Greens theorem.
LO05 Calculates surface integrals.
LO06 Prove the basic properties of divergence theorem.
LO07 Do the Diverjans theorem applications
LO08 Do the Green theorem applications.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. 5
PLO02 Bilgi - Kuramsal, Olgusal Understands importance of basic consepts of Algebra, Analaysis and Topology. 5
PLO03 Yetkinlikler - Öğrenme Yetkinliği Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. 5
PLO04 Bilgi - Kuramsal, Olgusal Demonstrate the ability to express the basic theories of mathematics both correctly. 5
PLO05 Bilgi - Kuramsal, Olgusal Understands the relationship between the different fields of mathematics and its relation to other disciplines. 4
PLO06 Bilgi - Kuramsal, Olgusal Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. 4
PLO07 Bilgi - Kuramsal, Olgusal Comprehend and explain mathematical models such as formulas, graphs, tables and schema. 3
PLO08 Bilgi - Kuramsal, Olgusal Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. 3
PLO09 Bilgi - Kuramsal, Olgusal Comprehends at least one of the computer programming languages.
PLO10 Bilgi - Kuramsal, Olgusal Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. 3
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. 4
PLO13 Yetkinlikler - Öğrenme Yetkinliği Understands the programming techniques and shows the ability to do programming.
PLO14 Yetkinlikler - Öğrenme Yetkinliği Demonstrates the ability to study mathematics both independently and as a group. 4
PLO15 Bilgi - Kuramsal, Olgusal Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. 3
PLO16 Bilgi - Kuramsal, Olgusal Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. 3
PLO17 Bilgi - Kuramsal, Olgusal It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. 4
PLO18 Bilgi - Kuramsal, Olgusal Gains the ability to use information technologies effectively for contemporary mathematical applications. 4
PLO19 Bilgi - Kuramsal, Olgusal Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. 4
PLO20 Bilgi - Kuramsal, Olgusal Gains the consciousness of prefesional ethics and responsibility. 5


Week Plan

Week Topic Preparation Methods
1 Limit and derivative of vector functions. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
2 Properties of the derivative of vector functions. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
3 Motion along curve: speed, acceleration vector and uniform circular motion. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
4 Tangential and normal compenents of the acceleration vector. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
5 Newton and Kepler laws. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
6 Vector and scalar fields and methods to obtain a new vector field from a vector field Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
7 Line integrals. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
8 Mid-Term Exam Review of the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
9 Some physical applications of line integrals. (the work done along the curve, total flux) Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
10 Proof of Greens theorem. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
11 Greens theorem for the regions bounded by two curves. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
12 Conservative vector fields and fundemental theorem of line integrals. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
13 Computation of surface integrals. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
14 Proof of the Divergence theorem. Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
15 Some applications of divergence theorem Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams Review of the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Review of the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 2 28
Out of Class Study (Preliminary Work, Practice) 14 2 28
Assesment Related Works
Homeworks, Projects, Others 1 0 0
Mid-term Exams (Written, Oral, etc.) 1 8 8
Final Exam 1 24 24
Total Workload (Hour) 88
Total Workload / 25 (h) 3,52
ECTS 4 ECTS