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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 co-requisites: 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 Up

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 Up
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 applications of Euler-Lagrange 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 Hamilton-Jacobi equation
Week 13: The classical mechanics applications of Hamilton-Jacobi equation
Week 14: The general relativity applications of Hamilton-Jacobi equation and 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 Up
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 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: 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)
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