GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION

DIFFERENTIABLE MANIFOLDS/4350219

Course Title:	DIFFERENTIABLE MANIFOLDS
Credits	3	ECTS	7.5
Semester	2	Compulsory/Elective	Elective

COURSE INFO

-- LANGUAGE OF INSTRUCTION

Turkish

-- NAME OF LECTURER(S)

Assoc.Prof. Hasan ES

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

http://www.websitem.gazi.edu.tr/site/hasanes

-- EMAIL(S) OF LECTURER(S)

hasanes@gazi.edu.tr

-- LEARNING OUTCOMES OF THE COURSE UNIT

To gain skills for relation analysis and learning about this lecture.

-- MODE OF DELIVERY

The mode of delivery of this course is Face to face

-- PREREQUISITES AND CO-REQUISITES

There is no prerequisite or co-requisite for this course.

-- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS

There is no recommended optional programme component for this course.

--COURSE CONTENT
1. Week	Shape operator
2. Week	A connection on a manifold.
3. Week	Gauss equation. Differential forms
4. Week	Orientation of manifolds
5. Week	Partition of unity. Curvature and torsion
6. Week	Connection forms
7. Week	Riemannian manifold
8. Week	Midterm Exam
9. Week	Riemann connection
10. Week	The geometry of surfaces in E3
11. Week	Submanifolds of Riemannian manifolds
12. Week	Hypersurfaces, Codazzi-Mainardi Equations
13. Week	integration on manifolds
14. Week	Lie groups.
15. Week	One-parameter groups acting on a manifold. Lie derivative.
16. Week	Final Exam

-- RECOMMENDED OR REQUIRED READING

Differensiyel Geometri, Prof.Dr. H.H. Hilmi Hacısalihoğlu Differensiyel Geometri, Prof.Dr. Arif Sabuncuoğlu Notes on Differential Geometry, N.J. Hicks Elemantary Differential Geometry, Baret O’Neil A Comprehensive Introtuction to Differential Geometry, M.Spivak

-- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS

Lecture, Question & Answer, Demonstration, Drill - Practise

-- WORK PLACEMENT(S)

-- ASSESSMENT METHODS AND CRITERIA

	Quantity	Percentage
Mid-terms	1	40
Assignment	0	0
Exercises	0	0
Projects	0	0
Practice	0	0
Quiz	0	0
Contribution of In-term Studies to Overall Grade		40
Contribution of Final Examination to Overall Grade		60

-- WORKLOAD

Efficiency	Total Week Count	Weekly Duration (in hour)	Total Workload in Semester
Theoretical Study Hours of Course Per Week	14	3	42
Practising Hours of Course Per Week			0
Reading	10	5	50
Searching in Internet and Library			0
Designing and Applying Materials			0
Preparing Reports	10	5	50
Preparing Presentation			0
Presentation			0
Mid-Term and Studying for Mid-Term	1	20	20
Final and Studying for Final	1	25	25
Other			0
TOTAL WORKLOAD:			187
TOTAL WORKLOAD / 25:			7.48
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
7				X
8
9
10					X

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GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR