Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 3 / Spring Semester | ||||
| Level of Course | 1st Cycle Degree Programme | ||||
| Type of Course | Compulsory | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | ESMA DEMİR ÇETİN (esma.demir@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | ESMA DEMİR ÇETİN, ÇAĞLA RAMİS, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| Giving basic information about differential geometry that the student will need during undergraduate and graduate education. And to figure out how to go about solving problems. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Know general properties of curves. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. PO-4 Analytically use the interdisciplinary approach at learning process. |
Examination |
| LO-2 | Know curvatures and line of curvatures. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| LO-3 | Know Riemann manifold,covariant derivative,hypersurfaces in En . |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| LO-4 | Know fundamental forms and shape operators. Solve problems with these. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Curve length, parameter change, Frenet frame and Frenet planes of curve, Curvature and torsion, Geometric meaning of curvatures, Helix, Special Curves and their characterizations, Introduction to Surface Theory, Shape Operator, Gauss Transform, Fundamental forms, Gauss and mean curvatures, Curve-surface frame, Principal curvatures and normal curvature, Regle surface | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Curve length, parameter change | Speech, Problem Solving |
| 2 | Frenet frame | Speech, Problem Solving |
| 3 | Frenet planes of curve | Speech, Problem Solving |
| 4 | Curvature and torsion | Speech, Problem Solving |
| 5 | Geometric meaning of curvatures | Speech, Problem Solving |
| 6 | Helix | Speech, Problem Solving |
| 7 | Special Curves and their characterizations | Speech, Problem Solving |
| 8 | mid-term exam | |
| 9 | Introduction to Surface Theory | Speech, Problem Solving |
| 10 | Shape Operator, Gauss Transform | Speech, Problem Solving |
| 11 | Fundamental forms | Speech, Problem Solving |
| 12 | Gauss and mean curvatures | Speech, Problem Solving |
| 13 | Curve-surface frame | Speech, Problem Solving |
| 14 | Principal curvatures and normal curvature | Speech, Problem Solving |
| 15 | Regle surface | Speech, Problem Solving |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Gray, A. Modern Differential Geometry, CRC Press LLC, 1998. | |
| 2 | Hacısalihoğlu, H.Hilmi. Diferensiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,2000. | |
| Required Course instruments and materials | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 14 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 4 | 14 | 56 |
| Outside Class | |||
| a) Reading | 3 | 10 | 30 |
| b) Search in internet/Library | 3 | 14 | 42 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 2 | 8 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 6 | 5 | 30 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 178 | ||