Differentiable Manifolds

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

-

Course Contents

Euclidean Space, Differential of Maps and Jacobien, Tangent Space, Derivative Map, Differential of a Vector field along a curve, Covariant derivatives, Lie product, Differential Manifols, Differential Maps, Submanifolds, Tangent space of a manifold, Grasmanian manifols, Vector fields on manifolds, Lie Algebra of a Manifold, Kotangent Space

Weekly Schedule

1) Euclidean space
2) Differentiation of transformations and Jacobian.
3) Tangent space
4) Derivative transformation
5) Differentiation of a vector field along a curve in E^n
6) Covariant derivative
7) Lie product
8) Midterm exam
9) Differentiable transformations
10) Differentiable manifold
11) Submanifolds
12) Tangent space at a point of a manifold
13) Vector fields on manifolds.
14) Lie algebra of a manifold
15) Cotangent space
16) Final exam

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Lecture
3) Question-Answer
4) Question-Answer
5) Discussion
6) Discussion
7) Drill and Practice
8) Drill and Practice
9) Brain Storming
10) Brain Storming
11) Self Study
12) Self Study
13) Problem Solving
14) Problem Solving

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	40%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required