Iğdır University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT-23-203	DIfferentIable MonIfolds II	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

Differentiable manifolds

Name of Lecturer(s)

Learning Outcomes

1	Understands forms on manifolds and uses them
2	Understands and uses the maps between manifolds; tangent spaces,vector fields

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

Recommended Optional Programme Components

Course Contents

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Topological Manifolds: Locally Euclidian Spaces, Second countability, Hausdorff Space
2	Compatibility of charts and smooth atlasses
3	Some examples of smooth manifols.
4	Differentiable functions on smooth manifolds.
5	Geometric tangent vectors on Euclidian spaces and derivations
6	Tangent vectors on manifolds and tangent spaces.
7	Differentiable maps between smooth manifolds and diffeomorphisms.
8	Differentials of smooth maps.
9	Coordinat frame of tangent space. The interpretations of tangent vectors as a velocity vectors of smooth curves
10	Submanifolds.
11	Embeddings, immersions, submersions.
12	Vector fields, vector bundles
13	Local expressions of vector fields, Lie brackets of vector fields, integral curves, F-related vector fields
14	Cotangent bundles, 1-forms, 1-form fields, Local expressions, pull-backs of 1-forms.

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Work Placement(s)

Workload Calculation

Contribution of Learning Outcomes to Programme Outcomes

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High