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Syllabus ( MATH 450 )


   Basic information
Course title: Rational Mechanics
Course code: MATH 450
Lecturer: Prof. Dr. Oğul ESEN
ECTS credits: 4
GTU credits: 3 (3+0+0)
Year, Semester: 3, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Elective
Language of instruction: Turkish
Mode of delivery: Face to face
Pre- and co-requisites: none
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.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Establish and utilizing the connection between mathematics and classical mechanics

    Contribution to Program Outcomes

    1. 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.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    4. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    5. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  2. Comprehend the fundamentals of symplectic geometry in Hamiltonian mechanics and perform basic calculations

    Contribution to Program Outcomes

    1. 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.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    4. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
   Contents Up
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: Midterm, Canonical Transformations.
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*: -
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.
Recommended readings: Goldstein, H. (1980). Classical mechanics 2nd ed. Reading, Penn., Addison-Wesley
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 9 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 3 14
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 8 1
Mid-term: 2 1
Personal studies for final exam: 8 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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