Syllabus ( MATH 408 )

Basic information


Course title: 
Calculus of Variations 
Course code: 
MATH 408 
Lecturer: 
Assist. Prof. Tuğba MAHMUTÇEPOĞLU

ECTS credits: 
5 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
4, Fall 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Compulsory

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
The teaching of Lagrange and Hamilton formalism and also the teaching of the applications of variational calculus to theoretical physics. 



Learning outcomes


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

This course teaches the variational calculus which is an important application of functional analysis.
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.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Variational calculus is an interdisciplinary course and gives the skill to mathematicians to collobrate with physicists.
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.

Ability to work in interdisciplinary research teams effectively.
Method of assessment

Written exam

In this course students learn the applications of variational calculus to theoretical physics.
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.
Method of assessment

Written exam


Contents


Week 1: 
Function and functional 
Week 2: 
Newton equation and the equations of motion of miscellanous systems 
Week 3: 
Lagrange equations as a different form of Newton equation 
Week 4: 
The formal derivation of EulerLagrange equations 
Week 5: 
The applications of EulerLagrange equations to classical mechanics 
Week 6: 
The applications of EulerLagrange equations to special and general relativity theory 
Week 7: 
The continuation of applications of EulerLagrange equations to relativity theory 
Week 8: 
Midterm exam and solutions 
Week 9: 
Hamilton formalism 
Week 10: 
The derivation of equations of motion as a result of Hamilton equations 
Week 11: 
The classical mechanics applications of Hamilton formalism 
Week 12: 
The derivation of HamiltonJacobi equation 
Week 13: 
The classical mechanics applications of HamiltonJacobi equation 
Week 14: 
The general relativity applications of HamiltonJacobi equation and PathIntegral formalism and its relation with quantum mechanics 
Week 15*: 
 
Week 16*: 
Final Exam 
Textbooks and materials: 
Mechanics, Keith R. Symon, Reading, Massachusets, AddisonWesley, 1971 A Short Course in General Relativity, J. Foster, J. D. Nightingale, SpringerVerlag, 1995. 
Recommended readings: 
Analytical Mechanics for Relativity and Quantum Mechanics, Oliver Davis Johns, Oxford University Press, 2005 Tensors, Differential Forms, and Variational Principles, David Lovelock and Hanno Rund, Dover Publications, New York, 1989 

* 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: 
8 
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: 
10 
1 

Midterm: 
3 
1 

Personal studies for final exam: 
10 
2 

Final exam: 
3 
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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