CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

INTRODUCTION TO DIFFERANTIAL GEOMETRY | MAT307 | FALL | 4+0 | C | 6 |

Learning Outcomes | 1-To describe the relationship between vector and directional derivative 2-To explain the concepts of vector field 3-To explain basic notions of curves |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 5 | 70 | |

Assignments | 10 | 2 | 6 | 12 |

Short-Term Exams (exam + preparation) | 10 | 2 | 6 | 12 |

Midterm exams (exam + preparation) | 30 | 1 | 14 | 14 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 180 | |||

Total Workload (hours) / 30 (s) | 6 ---- (6) | |||

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Affine space | |

2 | Euclidean space, Euclidean frame and coordination system | |

3 | Topolojic space, Metric space and relationship between E^n | |

4 | Differentiable functions | |

5 | Tangent plane and directional derivative | |

6 | Vector field | |

7 | The derivative transformation | |

8 | The definition of a curve and its parametric representations; velocity vector and its length, unit-speed curves | |

9 | Vector field along a curve | |

10 | Covariant derivative in the Euclidean space | |

11 | Serret-Frenet formulas of unit speed curves; curvatures and geometric comments | |

12 | Touching theory | |

13 | Serret- Frenet formulas of non-unit-speed curves | |

14 | Involute -Evolute, Bertnard curve pair and spherical indicatrix of a curve |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Celallettin Kaya |

Instructors |
1-)Doçent Dr Ufuk Öztürk |

Assistants | - |

Resources | Diferensiyel Geometri (4. Baskı), Arif Sabuncuoğlu, Nobel Akademik Yayıncılık, 2010. |

Supplementary Book | [1] Çözümlü Diferensiyel Geometri Alıştırmaları (2. Baskı), Arif Sabuncuoğlu, Nobel Akademik Yayıncılık, 2012. [2] Diferansiyel Geometri : Eğriler ve Yüzeyler, P. Do. Carmo Manfredo, Çeviren : Belgin Korkmaz, TÜBA Ders Kitapları Dizisi, Sayı : 8, 2012. [3] Diferensiyel Geometri Cilt : 1 (3. Baskı), H.Hilmi Hacısalihoğlu, Hacısalihoğlu Yayınları, Anakara, 1998. [4] Çözümlü Diferensiyel Geometri Problemleri Cilt : 1 (2. Baskı), H.Hilmi Hacısalihoğlu, Ertuğrul Özdamar, Cengizhan Murathan, Esen İyigün, Hacısalihoğlu Yayınları, Anakara, 2005 [5] A First Course in Geometric Topology and Differential Geometry, Ethan D. Block, Birkhauser, Boston, 1996. [6] Elementary Differential Geometry (Springer Undergraduate Mathematics Series) (2nd Edition), Andrew Pressley, Springer-Verlag, London, 2010. |

Document | Lecture notes |

Goals | To teach the basic notions and theorems of curves and surfaces in R^3 |

Content | - |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 5 |

2 | To have the ability of abstract thinking | 4 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 5 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 3 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 3 |

6 | To be able to work compatibly and effectively in national and international groups and take responsibility | - |

7 | To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge | 4 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 4 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | 2 |

10 | To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally | 4 |

11 | To be able to produce projects and arrange activities with awareness of social responsibility | - |

12 | To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level | - |

13 | To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results | - |

14 | To have the awareness of acting compatible with social, scientific, cultural and ethical values | - |

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