GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION

THEORY OF MANIFOLDS II/5461305

Course Title:	THEORY OF MANIFOLDS II
Credits	3	ECTS	7.5
Course Semester	1	Type of The Course	Elective

COURSE INFORMATION

-- (CATALOG CONTENT)

-- (TEXTBOOK)

-- (SUPPLEMENTARY TEXTBOOK)

-- (PREREQUISITES AND CO-REQUISITES)

-- LANGUAGE OF INSTRUCTION

Turkish

-- COURSE OBJECTIVES

-- COURSE LEARNING OUTCOMES

They learn the properties of vector field on a manifold
They can give the response of the derivative in analysis for the manifold
They learn a differential equation definition on a manifold
They learn Frobenius Theorem
They learn Lie group structure
They learn Lie algebra

-- MODE OF DELIVERY

The mode of delivery of this course is Face to face

--WEEKLY SCHEDULE
1. Week	Definitions and characteristic properties of vector fields, The tangent bundle.
2. Week	Independent vector fields,orientable manifolds
3. Week	Differentiable equations of first order definitions and examples, Maximal integral curves.
4. Week	Differentiable equations on a quotient manifold, eigenvalues of a vector field
5. Week	Lineer connections definitions and charecteristic properties, the curvature and torsion of a linear connection.
6. Week	The horizontal distribution, Riemannian connection.
7. Week	Differential equations of second order definitions and basic properties, Sprays
8. Week	The Riemannian Spray, The metric structure on a Riemannian Manifold
9. Week	Distributions definitions and examples, Frobenius Theorem
10. Week	Integral manifolds of a distribution, an application to linear connections
11. Week	Lie groups definitions and examples, some topological properties of Lie groups, Lie subgroups,the Lie algebra of a Lie Group
12. Week	The exponential mapping for a Lie Group, A special chart of a Lie Group
13. Week	Lie Transformation Groups definition and examples,A Lie algebra of vector fields
14. Week	Orbits under a Lie transformatin group, An exponential mapping
15. Week
16. Week

-- TEACHING and LEARNING METHODS

-- ASSESSMENT CRITERIA

	Quantity	Total Weighting (%)
Midterm Exams	1	20
Assignment	4	15
Application	0	0
Projects	0	0
Practice	0	0
Quiz	2	15

Percent of In-term Studies		50
Percentage of Final Exam to Total Score		50

-- WORKLOAD

Activity	Total Number of Weeks	Duration (weekly hour)	Total Period Work Load
Weekly Theoretical Course Hours	14	3	42
Weekly Tutorial Hours			0
Reading Tasks			0
Searching in Internet and Library	6	15	90
Material Design and Implementation			0
Report Preparing			0
Preparing a Presentation			0
Presentation			0
Midterm Exam and Preperation for Midterm Exam	1	20	20
Final Exam and Preperation for Final Exam	1	30	30
Other (should be emphasized)			0
TOTAL WORKLOAD:			182
TOTAL WORKLOAD / 25:			7.28
Course Credit (ECTS):			7.5

-- COURSE'S CONTRIBUTION TO PROGRAM

NO	PROGRAM LEARNING OUTCOMES	1	2	3	4	5
1					X
2					X
3				X
4					X
5			X
6						X
7
8				X
9						X
10
11
12		X

-- NAME OF LECTURER(S)

(Assoc.Prof. Mustafa ÖZKAN)

-- WEB SITE(S) OF LECTURER(S)

(http://websitem.gazi.edu.tr/site/ozkanm)

-- EMAIL(S) OF LECTURER(S)

(ozkanm@gazi.edu.tr)

Gazi University

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GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR