• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

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

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

   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. Exhibiting professional and ethical responsibility.

   Method of assessment

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

   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. Ability to work in interdisciplinary research teams effectively.

   Method of assessment

   1. Written exam
3. In this course students learn the applications of variational calculus to theoretical physics.

   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.

   Method of assessment

   1. 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 Euler-Lagrange equations.
Week 5:	The applications of Euler-Lagrange equations to classical mechanics.
Week 6:	The applications of Euler-Lagrange equations to special and general relativity theory.
Week 7:	The continuation of the applications of Euler-Lagrange equations to relativity.
Week 8:	Hamilton formalism. Midterm Exam.
Week 9:	The derivation of equations of motion as a result of Hamilton equations.
Week 10:	The classical mechanics applications of Hamilton formalism.
Week 11:	The derivation of Hamilton-Jacobi equation.
Week 12:	The classical mechanics applications of Hamilton-Jacobi equation.
Week 13:	The general relativity applications of Hamilton-Jacobi equation.
Week 14:	Path-Integral formalism and its relation with quantum mechanics.
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	Mechanics, Keith R. Symon, Reading, Massachusets, Addison-Wesley, 1971 A Short Course in General Relativity, J. Foster, J. D. Nightingale, Springer-Verlag, 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 (%)
Mid-terms:	8	40
Other in-term 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 (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:	10	1
Mid-term:	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)