Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
DIFFERENTIABLE MANIFOLDS I 801500715130 3 + 0 3.0 8.0

Prerequisites None

Language of Instruction Turkish
Course Level Graduate Degree
Course Type Compulsory
Mode of delivery Face to face
Course Coordinator
Instructors İsmail GÖK
Assistants
Goals The purpose of this course is to teach the basic concepts of manifold geometry.
Course Content Euclidean space, the differentiable maps and jacobien, the tangent space, derivative transformation, in En differentiable of a vector field along a curve , covariant derivative, Lie multiplication, differentiable manifolds, differentiable mappings, submanifolds, tangent space at a point of a manifold, Grassman manifolds, vector fields on manifolds, Lie algebra of a manifold, the cotangent space
Learning Outcomes 1) Teaches the fundamental concepts of the differential geometry.
2) Teaches the fundamental concepts of the differential geometry.
3) Have knowledge about the Riemann manifold
4) Have knowledge about the tensor algebra

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Differentiable manifolds, differentiable maps Lecture

 Presentation (Including Preparation Time)
2. Week Tangent vectors and tangent space, directional derivative Lecture

 Presentation (Including Preparation Time)
3. Week parametrization curve, cotangent space, covector, 1-form, dualite, tangent vecor and tangent space on manifold. Lecture

 Presentation (Including Preparation Time)
4. Week Coordinat transformation, functions algebra Lecture

 Presentation (Including Preparation Time)
5. Week Riemannian metric and Riemannian Manifold Lecture

 Presentation (Including Preparation Time)
6. Week directional derivative and critical points, Hess form of a function. Lecture

 Presentation (Including Preparation Time)
7. Week diferentiative of a map Lecture

 Presentation (Including Preparation Time)
8. Week algebra of the multilinear functioni tensor algebra of the vector spaces, tensors Lecture

 Presentation (Including Preparation Time)
9. Week covariant tensors, contravariant tensors, mix tensors Lecture

 Presentation (Including Preparation Time)
10. Week tensor algebra, symetric tensors, alterne tensors Lecture

 Presentation (Including Preparation Time)
11. Week exterior product and dimension of the exterior product Lecture

 Presentation (Including Preparation Time)
12. Week inner product tensor, the symmetric product, the symmetric algebra, Lecture

 Presentation (Including Preparation Time)
13. Week Product the real space Lecture

 Presentation (Including Preparation Time)
14. Week Isomorphic tensor spaces, tensor product of the linear transformations and linear endorfizm. Lecture

 Presentation (Including Preparation Time)

Sources Used in This Course
Recommended Sources
Diferensiyel Geometri, H. Hilmi Hacısalihoğlu, A. Ü. Fen fakültesi, II. Cilt, 1994 ; Diferensiyel Geometri, H. Hilmi Hacısalihoğlu, A. Ü. Fen fakültesi, III. Cilt, 2003

Relations with Education Attainment Program Course Competencies
Program RequirementsContribution LevelDK1DK2DK3
PY15000
PY25000
PY35000
PY45554
PY45433
PY45555
PY45533
PY45533
PY45544
PY45522
PY45512
PY45544
PY45000
PY45000
PY45544

*DK = Course's Contrubution.
0 1 2 3 4 5
Level of contribution None Very Low Low Fair High Very High
.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 16 3
Work Hour outside Classroom (Preparation, strengthening) 16 3
Homework 3 10
Midterm Exam 1 60
Time to prepare for Midterm Exam 1 2
Final Exam 1 50
Time to prepare for Final Exam 1 2
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
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Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • Relations with Education Attainment Program Course Competencies
  • ECTS credits and course workload