PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 514	DIFFERENTIABLE MANIFOLDS -II	3 + 0	2nd Semester	7,5

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.

COURSE LEARNING OUTCOMES

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

COURSE'S CONTRIBUTION TO PROGRAM

Data not found.

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	7	98
Assignments	1	5	5
Mid-terms	1	15	15
Final examination	1	35	35
Total Work Load ECTS Credit of the Course			195 7,5

COURSE DETAILS

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L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

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