Information Package / Course Catalogue
Tensor Geometry
Course Code: MTK549
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

The purpose of this course to to give students information about multilinear functions and tensor fields and to teach related concepts.

Course Content

Vector spaces, multilinear functions, tensor fields, covariant tensor fields, tensor derivative, Levi-Civita connection, curvature tensor, type-changing and metric contraction operators.

Name of Lecturer(s)
Lec. Seçkin GÜNSEN
Learning Outcomes
1.To be able to learn vector spaces and dual spaces.
2.To be able to define linear function and multilinear function
3.To be able to define tensor field
4.To be able to explain the concepts of tensor derivative, Levi-Civita connection and covariant differential.
5.To be able to make type-changing and metric contraction operations
Recommended or Required Reading
1.Semi-Riemannian Geometry with Application to Relativity, O’Neill,B., Academic Press.Inc.New York 1983
2.Hacısalihoğlu, H.Hilmi., Ekmekci,N.,Tensör Geometri Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,2004
3.Sabuncuoğlu, Arif, Diferensiyel Geometri, Nobel Yayınevi
Weekly Detailed Course Contents
Week 1 - Theoretical
Vector spaces, dual spaces
Week 2 - Theoretical
Multilinear functions
Week 3 - Theoretical
Tensor fields and the operations of tensor fields
Week 4 - Theoretical
Tensor components
Week 5 - Theoretical
Problem solving
Week 6 - Theoretical
Contraction and covariant tensors
Week 7 - Theoretical
Tensor derivations
Week 8 - Theoretical
Levi-Civita connection and covariant differential
Week 9 - Theoretical
Problem solving
Week 10 - Theoretical
Riemannian curvature tensor
Week 11 - Theoretical
Type-changing operators
Week 12 - Theoretical
Type-changing operators and metric contraction
Week 13 - Theoretical
Tensor fields applications with differential operators
Week 14 - Theoretical
Problem solving
Assessment Methods and Criteria
Type of AssessmentCountPercent
Final Examination1%70
Assignment3%30
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Assignment301236
Individual Work140570
Final Examination150252
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
2
1
2
2
1
2
3
OÇ-2
4
2
3
5
1
2
3
OÇ-3
2
1
3
2
1
2
3
OÇ-4
2
2
2
2
1
2
2
OÇ-5
2
2
2
2
1
2
2
Adnan Menderes University - Information Package / Course Catalogue
2026