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Course Title: |
DIFFERANTIAL GEOMETRY II |
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Course Code: |
MAT3016 |
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Type of Course: |
Compulsory |
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Level of Course: |
First Cycle |
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Year of Study: |
3 |
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Semester: |
6 |
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ECTS Credits Allocated: |
6 |
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Theoretical (hour/week): |
2 |
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Practice (hour/week) : |
2 |
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Laboratory (hour/week) : |
0 |
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Prerequisites: |
MAT 2013 Analytic Geometry I , MAT2014 Analytic Geometry II and MAT3015 Differential Geometry I |
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Recommended optional programme components: |
None |
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Language: |
Turkish |
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Mode of Delivery: |
Face to face |
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Course Coordinator: |
Prof. Dr. Kadri Arslan |
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Course Lecturers: |
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Contactinformation of the Course Coordinator: |
arslan@uludag.edu.tr
(0 224) 294 17 75
Uludağ Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
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Website: |
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Objective of the Course: |
The purpose of this course, graduate level students to teach the basic concepts of differential geometry. The student was identified with the Euclidean space and after that it is introduced the surface theory and the concept of surface types in this space. In addition, the concept of the surface has been handled and the tangent and normal vector on the surfaces, forms, topological properties of surfaces and surface ransformations are introduced. Curvatures of surfaces with the help of the calculation aim to understanding the geometric meaning of the surfaces. |
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Contribution of the Course to Professional Development |
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Theoretical |
Practical |
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Patchs in the Rn, regular patch and the surface are defined. |
Some examples of a patch are given |
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Calculations of the patch and examples of patches are handled. |
Some examples of a surface are given |
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Tangent and normal vectors and differentiable functions are analyzed.
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Some examples of a tangent and normal vectors are given |
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Differential forms on surfaces are exprressed. |
Some examples of a differentiable forms are given |
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Mapping on the surfaces is given. Derivative transformation, transformations of the lower star and top stars are examined. |
Some examples of a derivative transformation are given |
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Focuses on issues of integration of forms and topological properties of surfaces. |
Some examples of a transformations of the lower star and top stars are given |
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Repeating courses and midterm exam |
Some examples of surfaces are considered |
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Shape operator and the normal curvature of the surfaces are considered. |
Some examples of shape operator are given |
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Gaussian and mean curvatures of the surfaces are treated with the definition and basic theorems about them. |
Some examples of normal curvature are given |
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computation techniques of Gaussian and mean curvature are given. |
Some examples of Gaussian and mean curvature are given |
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Some special curves on surfaces are examined. |
Some examples of curves on surfaces are given |
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Gaussian and mean curvatures of a surface of revolution and ruled surface are characterized. |
Some examples of ruled surface and surface of revolution are given |
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Levi-Civita derivative and geodesic lines on surface are discussed. |
Some examples of Levi-Civita derivative are given |
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On the intrinsic geometry of surfaces examined. |
Some examples of geometry on surfaces are given |
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Textbooks, References and/or Other Materials: |
O’Neill, B., Elementary Differential Geometry, Academic Press, New York, 1966.
G . Gray, A. “Modern Differential Geometry of Curves and Surfaces”. CRC Press, Boca Raton Ann Abor London Tokyo, 1993.
Andrew Pressley, Elemantary Differential Geometry, Springer-Verlag London Limited, Great Britain, 2001.
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Assesment |
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