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 corequisites: 
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


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

Establish and utilizing the connection between mathematics and classical mechanics
Contribution to Program Outcomes

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.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Comprehend the fundamentals of symplectic geometry in Hamiltonian mechanics and perform basic calculations
Contribution to Program Outcomes

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.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam


Contents


Week 1: 
Vector Spaces, Linear Independence. 
Week 2: 
Linear Transformations, Dual Spaces. 
Week 3: 
Bilinear Transformations, Musical Mappings and Nondegeneracy. 
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: 
LiePoisson 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., AddisonWesley 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
9 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 

0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface 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 midterm exam: 
8 
1 

Midterm: 
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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