Syllabus ( MATH 450 )
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Basic information
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Course title: |
Rational Mechanics |
Course code: |
MATH 450 |
Lecturer: |
Prof. Dr. Oğul ESEN
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ECTS credits: |
4 |
GTU credits: |
3 (3+0+0) |
Year, Semester: |
4, Spring |
Level of course: |
First Cycle (Undergraduate) |
Type of course: |
Elective
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Language of instruction: |
English
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Mode of delivery: |
Face to face
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Pre- and co-requisites: |
Math 111 or Math 101 |
Professional practice: |
No |
Purpose of the course: |
The purpose of this course is to equip students with the skills to comprehend and analyze advanced topics in mathematics and theoretical physics by covering subjects in linear algebra, symplectic linear algebra, and Hamiltonian mechanics. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Establish and utilizing the connection between mathematics and classical mechanics
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
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Exhibiting professional and ethical responsibility.
Method of assessment
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Written exam
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Comprehend the fundamentals of symplectic geometry in Hamiltonian mechanics and perform basic calculations
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
Method of assessment
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Written exam
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Contents
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Week 1: |
Vector Spaces, Linear Independence. |
Week 2: |
Linear Transformations, Dual Spaces. |
Week 3: |
Bilinear Transformations, Musical Mappings and Non-degeneracy. |
Week 4: |
Differential of a map between vector spaces. |
Week 5: |
Symplectic Vector Spaces, Subspaces. |
Week 6: |
Symplectic Transformations, Symplectic Algebra. |
Week 7: |
Hamilton’s Equations on Symplectic Spaces. |
Week 8: |
Infinitesimal Symplectic Transformations. |
Week 9: |
Canonical Transformations. Midterm Exam. |
Week 10: |
Poisson Spaces. |
Week 11: |
Poisson Algebra (of Smooth Functions) and Hamilton’s Equations. |
Week 12: |
Poisson Dynamics in 3D and 4D. |
Week 13: |
Lie Algebras. |
Week 14: |
Lie-Poisson brackets and Hamilton's equations. |
Week 15*: |
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Week 16*: |
Final Exam. |
Textbooks and materials: |
Marsden, J. E. (1994). TS Ratiu Introduction to Mechanics and Symmetry. Texts in Applied Mathematics, 17. Springer Holm, D. D., Schmah, T., & Stoica, C. (2009). Geometric mechanics and symmetry: from finite to infinite dimensions Oxford University Press.
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Recommended readings: |
Goldstein, H. (1980). Classical mechanics 2nd ed. Reading, Penn., Addison-Wesley |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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Method of assessment |
Week number |
Weight (%) |
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Mid-terms: |
9 |
40 |
Other in-term studies: |
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0 |
Project: |
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0 |
Homework: |
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0 |
Quiz: |
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0 |
Final exam: |
16 |
60 |
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Total weight: |
(%) |
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Workload
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Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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Courses (Face-to-face teaching): |
3 |
14 |
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Own studies outside class: |
3 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
0 |
0 |
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Term project: |
0 |
0 |
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Term project presentation: |
0 |
0 |
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Quiz: |
0 |
0 |
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Own study for mid-term exam: |
8 |
1 |
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Mid-term: |
2 |
1 |
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Personal studies for final exam: |
8 |
1 |
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Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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