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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 514DIFFERENTIABLE MANIFOLDS -II3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective Giving the structure of the submanifold and learning tensors with the different manifold structures.
Course Content Maximal integral curves, flow of a vector field, differentiable equations on a quotient manifold, linear connections, horizontal distribution, Riemann connections, sprays, the metric structure on a Riemann manifold, distributions, reguler distributions, Lie algebra and groups, orbits under a Lie transformation group, groups of transformations of a Hausdorff manifold, automorphisms of a parallelization.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns maximal integral curves and knows flux of vector space, differentiable equations on section manifold.
2Knows linear connection, horizontal distribution, Riemann connection, spray and Riemann spray.
3Learns metric structure on Riemann manifolds, distributions, Regular distributions, realized Lie algebra and groups.
4Realized orbits in Lie transformation groups, groups of transformations of a hausdorff manifolds and knows otomorphizm of parallelism.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0015 45    
LO 0024 54    
LO 0035 54    
LO 0044 45    
Sub Total18 1818    
Contribution50550000

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2014-2015 Spring1CANSEL AYCAN
Details 2013-2014 Spring1CANSEL AYCAN
Details 2011-2012 Spring1CANSEL AYCAN
Details 2010-2011 Spring1CANSEL AYCAN
Details 2009-2010 Spring1CANSEL AYCAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 514 DIFFERENTIABLE MANIFOLDS -II 3 + 0 1 Turkish 2014-2015 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr FEN A0304 %70
Goals Giving the structure of the submanifold and learning tensors with the different manifold structures.
Content Maximal integral curves, flow of a vector field, differentiable equations on a quotient manifold, linear connections, horizontal distribution, Riemann connections, sprays, the metric structure on a Riemann manifold, distributions, reguler distributions, Lie algebra and groups, orbits under a Lie transformation group, groups of transformations of a Hausdorff manifold, automorphisms of a parallelization.
Topics
WeeksTopics
1 structure of manifold
2 structure of submanifold
3 tensors
4 algebra of tensörs
5 symetric product and external product
6 lie Groups
7 algebra of lie Groups
8 roof beams
9 midterm exam
10 Maximal integral curves
11 flow of a vector field
12 manifold varieties
13 trend lines, curvatures
14 fınal exam
Materials
Materials are not specified.
Resources
ResourcesResources Language
yüksek diferensiyel geometriye giriş, H.H HacısalihoğluTürkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes