COURSE SYLLABUS
THEORY OF TANGENT AND COTANGENT BUNDLES
| 1 |
Course Title: |
THEORY OF TANGENT AND COTANGENT BUNDLES |
| 2 |
Course Code: |
MAT6329 |
| 3 |
Type of Course: |
Optional |
| 4 |
Level of Course: |
Third Cycle |
| 5 |
Year of Study: |
1 |
| 6 |
Semester: |
1 |
| 7 |
ECTS Credits Allocated: |
6 |
| 8 |
Theoretical (hour/week): |
3 |
| 9 |
Practice (hour/week) : |
0 |
| 10 |
Laboratory (hour/week) : |
0 |
| 11 |
Prerequisites: |
|
| 12 |
Recommended optional programme components: |
None |
| 13 |
Language: |
Turkish |
| 14 |
Mode of Delivery: |
Face to face |
| 15 |
Course Coordinator: |
Prof. Dr. CENGIZHAN MURATHAN |
| 16 |
Course Lecturers: |
|
| 17 |
Contactinformation of the Course Coordinator: |
cengiz@uludag.edu.tr |
| 18 |
Website: |
|
| 19 |
Objective of the Course: |
Learn bundle theory. |
| 20 |
Contribution of the Course to Professional Development |
The student learns lift theory. |
| 21 |
Learning Outcomes: |
| 1 |
Learn tanjan bundle theory;
|
| 2 |
Learn complete ant vertical lift;
|
| 3 |
Learn horizontal lift;
|
| 4 |
Learn Sasalk metric on tanjant bundle;
|
| 5 |
Learn cotanjant bundle;
|
| 6 |
Learn vertical and horizontal lift of forms;
|
|
| Week |
Theoretical |
Practical |
| 1 |
Tanjant bundle |
|
| 2 |
Vertical lift and complete lift |
|
| 3 |
Lift derivations |
|
| 4 |
Lie derivatievs |
|
| 5 |
Horizontal lifts of functions and vector fields |
|
| 6 |
Horizontal lifts of tensor fields |
|
| 7 |
Almost complex structures in a Tanajant bundle |
|
| 8 |
Metrics on tanjant bundle |
|
| 9 |
Cotanjant bundle |
|
| 10 |
complete lifts of forms |
|
| 11 |
Comple lifts of Derivations on Cotanjant bundle |
|
| 12 |
Almost complex structures in the cotanjant bundle |
|
| 13 |
Prolangations of tensor fields |
|
| 14 |
Jet bundles |
|
| 23 |
Textbooks, References and/or Other Materials: |
Yano K, Ishihara S, (1973). Tangent and Cotangent Bundles. Marcel
Dekker, Inc., New York. |
| 24 |
Assesment |
|
| TERM LEARNING ACTIVITIES |
NUMBER |
PERCENT |
| Midterm Exam |
0 |
0 |
| Quiz |
0 |
0 |
| Homeworks, Performances |
0 |
0 |
| Final Exam |
1 |
100 |
| Total |
1 |
100 |
| Contribution of Term (Year) Learning Activities to Success Grade |
0 |
| Contribution of Final Exam to Success Grade |
100 |
| Total |
100 |
| Measurement and Evaluation Techniques Used in the Course |
The system of relative evaluation is applied |
| Information |
|
| 25 |
|
ECTS / WORK LOAD TABLE |
| Activites |
NUMBER |
TIME [Hour] |
Total WorkLoad [Hour] |
| Theoretical |
14 |
3 |
42 |
| Practicals/Labs |
0 |
0 |
0 |
| Self Study and Preparation |
11 |
11 |
121 |
| Homeworks, Performances |
0 |
0 |
0 |
| Projects |
0 |
0 |
0 |
| Field Studies |
0 |
0 |
0 |
| Midtermexams |
0 |
0 |
0 |
| Others |
1 |
10 |
10 |
| Final Exams |
1 |
7 |
7 |
| Total WorkLoad |
|
|
180 |
| Total workload/ 30 hr |
|
|
6 |
| ECTS Credit of the Course |
|
|
6 |
| 26 |
CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS |
|
PQ1
|
PQ2
|
PQ3
|
PQ4
|
PQ5
|
PQ6
|
PQ7
|
PQ8
|
PQ9
|
PQ10
|
|
LO1
|
3
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
LO2
|
0
|
4
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
LO3
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
LO4
|
0
|
0
|
0
|
4
|
0
|
0
|
0
|
0
|
0
|
0
|
|
LO5
|
0
|
0
|
0
|
4
|
0
|
0
|
0
|
0
|
0
|
0
|
|
LO6
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
| LO: Learning Objectives |
PQ: Program Qualifications |
| Contribution Level: |
1 Very Low |
2 Low |
3 Medium |
4 High |
5 Very High |
