Akademik Dersler - Tanıtım


Code - Course Title	MAT533 - Differentiable Manifolds
Course Type	Elective Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	7.5
Course Instructor(s)	PROFESÖR DOKTOR NEDİM DEĞİRMENCİ
Mode of Delivery	The mode of delivery of this course is only Face to face
Prerequisites	There is no prerequisite or co-requisite for this course.
Courses Recomended	Topology, Analysis
Required or Recommended Resources	1. Loring W. Tu, An Introduction to Manifolds, Springer, 2011.2. John Lee, Introduction to Smooth Manifolds, Springer, 2012.
Recommended Reading List	-
Assessment methods and criteria	Written exam
Work Placement	N/A
Sustainability Development Goals

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

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
1.Midterm Exam	1	40
Final Exam	1	60
Toplam (%)		100