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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 544TENSOR GEOMETRY AND APPLICATIONS I3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective The goal of the course is to make applications about lagrange systems using tensor on manifolds.
Course Content Introduction toTensor Geometry, Non-Euclidean Geometries, Geometry of Space Curves, Rn Geodesics, Geodesic Coordinates, Tensor Derivatives, Fundamental Concepts on Analytic Mechanics, Applications of Lagrange Equations.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns tensor geometry, knows geometry of space curves.
2Realized Rn geodesics, geodesic coordinate and tensor derivatives.
3Learns the basic concepts and Lagrange equations applications.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0015 4    4
LO 0024 55   4
LO 0035 44   5
Sub Total14 139   13
Contribution50430004

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 2022-2023 Fall1CANSEL AYCAN
Details 2010-2011 Fall1MEHMET TEKKOYUN
Details 2009-2010 Fall1MEHMET TEKKOYUN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 544 TENSOR GEOMETRY AND APPLICATIONS I 3 + 0 1 Turkish 2022-2023 Fall
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr FEN A0316 %70
Goals The goal of the course is to make applications about lagrange systems using tensor on manifolds.
Content Introduction toTensor Geometry, Non-Euclidean Geometries, Geometry of Space Curves, Rn Geodesics, Geodesic Coordinates, Tensor Derivatives, Fundamental Concepts on Analytic Mechanics, Applications of Lagrange Equations.
Topics
WeeksTopics
1 structure of manifold
2 system of frenets
3 frenet roofs
4 curvatures
5 tensors
6 christoffel symbols
7 mechanical systems
8 applications of mechanical systems
9 midterm exam
10 jet manifolds
11 jet bundles and its applications
12 minimal surfaces
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