TÜRKÇE
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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT236 |
| Name | Vector Analysis |
| Term | 2018-2019 Academic Year |
| 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 |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
| Course Instructor |
Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
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
Resources
Calculus and Analytic Geometry, Authors: Shermann K. Stein, Anthony Barcellos.
Notes
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 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 5 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 1 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 4 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 3 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 2 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 1 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 1 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 0 |
| PLO12 | - | 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. | 0 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 0 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 2 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 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 | Mid-Term 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 Greens theorem. | Review of the relevant pages from sources | |
| 11 | Greens 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 | Term Exams | Review of the topics discussed in the lecture notes and sources | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||