arslan@uludag.edu.tr (0 224) 294 17 75 Bursa Uludağ Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
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Website:
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Objective of the Course:
The aim of this course is to introduce the concept of manifold and give definitions of immersion and submersion.
also operations on manifolds and Lie algebra concepts are given.
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Contribution of the Course to Professional Development
It contributes to carrying the concepts in differential geometry to higher dimensions and applying the concept of submanifold.
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Learning Outcomes:
1
Knows the definition of differentiable manifolds and interprets examples of immersions
;
2
Knows the physics applications of Vector Fields and Flows.;
3
Make calculations about Lie Subgroups and Homogeneous Spaces.;
4
Can give examples by expressing vector bundles;
5
Interprets the results about Differential Forms;
6
Can perform integral calculations on manifolds.;
7
Can understand how De Rham cohomology is expressed;
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Can understand conclusions about cohomology with compact supports and Poincar´e duality.;
9
Interpret the De Rham cohomology concepts of compact manifolds.;
10
Can make calculations about pseudo Riemann metrics and Levi Civita covariant derivative.
;
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Course Content:
Week
Theoretical
Practical
1
Differentiable Manifolds .
2
Submersions and Immersions
3
Vector Fields and Flows
4
Lie Groups I
5
Lie Groups II. Lie Subgroups and Homogeneous Spaces
6
Vector Bundles
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Differential Forms
8
Integration on Manifolds
9
De Rham cohomology
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Cohomology with compact supports and Poincar´e duality
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De Rham cohomology of compact manifolds
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Lie groups III. Analysis on Lie groups
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Pseudo Riemann metrics and the Levi Civita covariant derivative
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Riemann geometry of geodesics
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Textbooks, References and/or Other Materials:
Michor P.W. - Topics in Differential Geometry (2006) - libgen.lc
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Assesment
TERM LEARNING ACTIVITIES
NUMBER
PERCENT
Midterm Exam
0
0
Quiz
0
0
Homeworks, Performances
2
50
Final Exam
1
50
Total
3
100
Contribution of Term (Year) Learning Activities to Success Grade
50
Contribution of Final Exam to Success Grade
50
Total
100
Measurement and Evaluation Techniques Used in the Course
The system of relative evaluation is applied.
Information
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ECTS / WORK LOAD TABLE
Activites
NUMBER
TIME [Hour]
Total WorkLoad [Hour]
Theoretical
14
3
42
Practicals/Labs
0
0
0
Self Study and Preparation
14
5
70
Homeworks, Performances
2
20
40
Projects
0
0
0
Field Studies
0
0
0
Midtermexams
0
0
0
Others
0
0
0
Final Exams
1
25
25
Total WorkLoad
177
Total workload/ 30 hr
5,9
ECTS Credit of the Course
6
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CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
