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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT321 |
| Name | Differential Geometry |
| Term | 2018-2019 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 8 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NERGİZ POYRAZ |
| Course Instructor |
Prof. Dr. DOĞAN DÖNMEZ
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To teach theories and applications about classical and generalized Stokes theorems, to give basic knowledge of curves and surfaces theories, to gain the ability of using analytical geometry, vector calculus and linear algebra knowledge, to teach understanding of abstract mathematical concepts and abstract thinking.
Course Content
Classical Stokes theorem and some applications, diferential forms and pull-back of diferential forms under diferentiable functions, Generalized Stokes theorem, curves and characterization of curves by curvature and torsion, Diferentiable surfaces and ruled surfaces.
Course Precondition
Resources
Calculus and Analytic Geometry, Authors:Shermann K. Stein, Anthony Barcellos.<br> A Geometric Approach to Diferential Forms, David Bachman <br> Differential Geometry, Martin M. Lipschitz (Schaum´s outline series)
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Solves the problems about classical Stokes theorem. |
| LO02 | Explains the concept of differential forms in space and cubical simplexes. |
| LO03 | Explains the generalized Stokes theorem. |
| LO04 | Recognizes the basic theorems about space curves. |
| LO05 | Recognizes isometries and the group of isometries of space. |
| LO06 | Recognizes the basic theorems about differentiable surfaces. |
| LO07 | Recognizes Implicit Function Theorem. |
| LO08 | Recognizes ruled surfaces. |
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. | 4 |
| 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. | 5 |
| 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. | 5 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 0 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| 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. | 3 |
| 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 | A brief introduction to Green s theorem, divergence theorem and surface integral | Review of the relevant pages from sources | |
| 2 | Classical Stokes theorem | Review of the relevant pages from sources | |
| 3 | Differential forms and exterior derivative of differential forms | Review of the relevant pages from sources | |
| 4 | Pull back of diferential forms under differentiable functions | Review of the relevant pages from sources | |
| 5 | Generalised Stokes theorem | Review of the relevant pages from sources | |
| 6 | The theory of curves and reparametrization by arc length | Review of the relevant pages from sources | |
| 7 | Curvature, torsion and Frenet-Serre equations | Review of the relevant pages from sources | |
| 8 | Mid-term exam | Review of the topics discussed in the lecture notes and sources | |
| 9 | Central curves, helices and involutes | Review of the relevant pages from sources | |
| 10 | Isometries and isometry group of space | Review of the relevant pages from sources | |
| 11 | Characterization of a curve by curvature and torsion | Review of the relevant pages from sources | |
| 12 | Characterization of a plane curve by curvature | Review of the relevant pages from sources | |
| 13 | Differentiable surfaces and implict function theorem | Review of the relevant pages from sources | |
| 14 | Ruled surfaces | Review of the relevant pages from sources | |
| 15 | Solving problems | Review of the relevant pages from sources | |
| 16 | Final exam | Review of the topics discussed in the lecture notes and sources | |
| 17 | Final exam | 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 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 8 | 112 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 4 | 8 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 212 | ||
| Total Workload / 25 (h) | 8,48 | ||
| ECTS | 8 ECTS | ||