Information Package / Course Catalogue
Differential and Riemannian Manifolds I
Course Code: MTK631
Course Type: Area Elective
Couse Group: Third Cycle (Doctorate Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

The main goal is this course to provide a working knowledge of Riemanniann manifolds, tensors and differential forms.

Course Content

Submanifold and Immersions, Tangent Bundles, Vector Fields and Differantial Operator, Lie Derivative, Killing Vector Fields, Mertirc Derivative.

Name of Lecturer(s)
Learning Outcomes
1.Ability to learn submanifolds and immersions
2.Ability to learn operations on vector fields
3.Ability to learn Lie derivative
4.Ability to learn killing vector fields
5.Ability to learn metric derivative
Recommended or Required Reading
1.Differential and Riemannian Manifolds, Lang S., Springer-Verlag 1995
Weekly Detailed Course Contents
Week 1 - Theoretical
Basic Properties
Week 2 - Theoretical
Defination of a Manifold
Week 3 - Theoretical
Submanifolds and Immersions
Week 4 - Theoretical
Solve the problem about what she/he has learned
Week 5 - Theoretical
Tangent Bundle
Week 6 - Theoretical
Operations on Vector Bundles
Week 7 - Theoretical
Vector Fields and Differantial Operators
Week 8 - Theoretical
Lie Derivative (MIDTERM EXAM)
Week 9 - Theoretical
Killing Vector Fields
Week 10 - Theoretical
Covariant Derivative
Week 11 - Theoretical
Solve the problem about what she/he has learned
Week 12 - Theoretical
Metric
Week 13 - Theoretical
The Metric Derivative
Week 14 - Theoretical
Solve the problem about what she/he has learned
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Quiz1%10
Midterm Examination1%15
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141356
Assignment101212
Individual Work140456
Quiz113215
Midterm Examination125227
Final Examination132234
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
3
3
3
3
3
2
OÇ-2
3
3
3
2
3
2
OÇ-3
3
3
3
3
2
OÇ-4
3
3
3
3
2
OÇ-5
4
5
3
3
4
3
3
3
2
Adnan Menderes University - Information Package / Course Catalogue
2026