CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

COMPLEX ANALYSIS II | MAT302 | SPRING | 4+0 | Fac./ Uni. | C | 8 |

Learning Outcomes | 1-To be able to describe the relationship between vector and directional derivative 2-To be able to explain the concepts of vector field and cotangent vector field 3-To be able to explain basic notions of curves 4-To be able to explain basic notions of surfaces |

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

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

Classroom study (Pre-study, practice) | 14 | 8 | 112 | |

Assignments | 10 | 2 | 8 | 16 |

Short-Term Exams (exam + preparation) | 10 | 2 | 8 | 16 |

Midterm exams (exam + preparation) | 30 | 1 | 12 | 12 |

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) | 228 | |||

Total Workload (hours) / 30 (s) | 7,6 ---- (8) | |||

ECTS Credit | 8 |

Week | Topics | Study Metarials |

1 | Tangent plane and directional derivative | |

2 | Differential of a map | |

3 | Vector field and cotangent vector field | |

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

5 | The derivative of a vector field along a curve | |

6 | Covariant derivative in the Euclidean space | |

7 | Tangent, normal, and binormal vectors; the notion of curvature and its geometric interpretation | |

8 | Osculating, rectifying, and normal planes; the notion of torsion and its geometric interpretation | |

9 | Non-unit-speed curves; the fundamental theorem of curves | |

10 | The definition and examples of surface; Monge surface and the notion of regular value | |

11 | The parametric curves on a surface; normal vector and tangent space of a surface | |

12 | Smooth functions on a surface and directional derivative | |

13 | A vector field on a surface | |

14 | Covariant derivative on a surface |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Süleyman CENGİZ |

Instructors | - |

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. Diferensiyel Geometri Cilt : 2 (3. Baskı), H.Hilmi Hacısalihoğlu, Hacısalihoğlu Yayınları, Anakara, 2000 5. Çözümlü Diferensiyel Geometri Problemleri Cilt : 1 (2. Baskı), H.Hilmi Hacısalihoğlu, Ertuğrul Özdamar, Cengizhan Murathan, Esen İyigün, Hacısalihoğlu Yayınları, Anakara, 2005 6. Çözümlü Diferensiyel Geometri Problemleri Cilt : 2, H.Hilmi Hacısalihoğlu, Yusuf Yaylı, Nejat Ekmekçi, Cengizhan Murathan, Ertuğrul Özdamar, Hacısalihoğlu Yayınları, Anakara, 1996 7. A First Course in Geometric Topology and Differential Geometry, Ethan D. Block, Birkhauser, Boston, 1996 8. Elementary Differential Geometry (Springer Undergraduate Mathematics Series) (2nd Edition), Andrew Pressley, Springer-Verlag, London, 2010 |

Document | - |

Goals | To teach the basic notions and theorems of curves and surfaces in R^3, to consolidate and to relate basic knowledge learned in analysis and linear algebra courses by applying them to geometry |

Content | Tangent plane and directional derivative; Differential of a map; Vector field and cotangent vector field; The definition of a curve and its parametric representations; Velocity vector and its length, unit-speed curves; The derivative of a vector field along a curve; Covariant derivative in the Euclidean space; Tangent, normal, and binormal vectors; The notion of curvature and its geometric interpretation; Osculating, rectifying, and normal planes; The notion of torsion and its geometric interpretation; Non-unit-speed curves; The fundamental theorem of curves; The definition and examples of surface; Monge surface and the notion of regular value; The parametric curves on a surface; Normal vector and tangent space of a surface; Smooth functions on a surface and directional derivative; A vector field on a surface; Covariant derivative on a surface |

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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