Information Package / Course Catalogue
Differential and Riemannian Manifolds II
Course Code: MTK632
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

The Riemannian Distance, Operations on Vector Fields, The Riemannian Volume Form, Stoke’s Theorem on a Manifold.

Name of Lecturer(s)
Learning Outcomes
1.Ability to learn the Riemannian distance
2.Ability to learn the second variation formula
3.Ability to learn Riemannian volume form
4.Ability to learn Stoke’s Theorem on a manifold
5.Ability to gain the skill of interpreting some interrelations among these concepts
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
The Riemannian Distance
Week 3 - Theoretical
The Riemannian Tensor
Week 4 - Theoretical
The Second Variation Formula
Week 5 - Theoretical
The Riemannian Volume Form
Week 6 - Theoretical
Covariant Derivatives
Week 7 - Theoretical
Solve the problem about what he has learned
Week 8 - Theoretical
The Jacobian Determinant of Exponential Map (MIDTERM EXAM)
Week 9 - Theoretical
Covariant Derivatives
Week 10 - Theoretical
Solve the problem about what he has learned
Week 11 - Theoretical
Orientation
Week 12 - Theoretical
Stoke’s Theorem on a Manifold
Week 13 - Theoretical
Divergence Theorem
Week 14 - Theoretical
Solve the problem about what 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