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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 513DIFFERENTIABLE MANIFOLDS -I3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Doctorate Degree
Course Type Elective
Course Objective Manifolds on the development of the basic geometric and topological concepts.
Course Content Differential manifolds and functions, induced topology on a manifold, varieties, Grassmann manifolds, Manifold structure on a topological space, properties of an induced topology, partitions of unity, tengent vectors, derived linear functions, immersions, submanifolds and some topological properties, reguler submanifolds, submersions and fibres, quotient manifolds, transformations groups, tangent bundle, vector fields, orientable manifolds.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns differentiable manifolds and functions, knows reduced topology on a manifold, varieties, Grasman manifolds.
2Learns manifold structure on a topological space, properties of the reduced topology, unit breakdown of unit.
3Learns tangent vectors, derivatived linear functions, immersions, submanifold and some topological properties.
4Knows regular submanifolds, submersiyonlar and fibers, section manifolds, transformation groups.
5Knows tangent bundle, vector fields, directional manifolds.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0015 44   5
LO 0024 54   4
LO 0035 45   5
LO 0045 44   5
LO 0054 55   4
Sub Total23 2222   23
Contribution50440005

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 2023-2024 Fall1CANSEL AYCAN
Details 2021-2022 Spring1CANSEL AYCAN
Details 2019-2020 Spring1CANSEL AYCAN
Details 2016-2017 Fall1CANSEL AYCAN
Details 2014-2015 Fall1CANSEL AYCAN
Details 2013-2014 Fall1CANSEL AYCAN
Details 2011-2012 Fall1CANSEL AYCAN
Details 2010-2011 Fall1CANSEL AYCAN
Details 2009-2010 Fall1CANSEL AYCAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 513 DIFFERENTIABLE MANIFOLDS -I 3 + 0 1 Turkish 2023-2024 Fall
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr FEN A0216 %70
Goals Manifolds on the development of the basic geometric and topological concepts.
Content Differential manifolds and functions, induced topology on a manifold, varieties, Grassmann manifolds, Manifold structure on a topological space, properties of an induced topology, partitions of unity, tengent vectors, derived linear functions, immersions, submanifolds and some topological properties, reguler submanifolds, submersions and fibres, quotient manifolds, transformations groups, tangent bundle, vector fields, orientable manifolds.
Topics
WeeksTopics
1 inner product spaces,Multilinear algebra
2 rigid motions(rotational, translational)
3 topological manifolds
4 differentiable manifolds
5 product and quotient manifolds
6 tangent vectors and tangent space
7 lie algebra and lie bracket
8 middterm exam
9 differential relative to the direction
10 cotangent space, covector, 1-forms
11 Riemannian metric and Riemannian manifolds
12 tensors and tensor algebra
13 covariant, contravariant and mixed tensors
14 final 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