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

Learning outcomes

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

1. The mathematical structure of Newton equation

   Contribution to Program Outcomes

   1. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

   Method of assessment

   1. Written exam
   2. Homework assignment
2. The determination of particle orbits via Newton equation.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Work effectively in multi-disciplinary research teams
   4. Develop mathematical, communicative, problem-solving, brainstorming skills.
   5. Effectively express his/her research ideas and findings both orally and in writing
   6. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
3. Lagrange function and the application of Euler-Lagrange equations in Classical Mechanics.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Acquire scientific knowledge and work independently
   4. Develop mathematical, communicative, problem-solving, brainstorming skills.
   5. Effectively express his/her research ideas and findings both orally and in writing
   6. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
4. The Determination of the orbits of planets under the influence of Gravitational force.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Acquire scientific knowledge and work independently
   4. Work effectively in multi-disciplinary research teams
   5. Develop mathematical, communicative, problem-solving, brainstorming skills.
   6. Effectively express his/her research ideas and findings both orally and in writing
   7. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
5. The learning of the basic concepts of Special and General Relativity theory.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Acquire scientific knowledge and work independently
   4. Work effectively in multi-disciplinary research teams
   5. Develop mathematical, communicative, problem-solving, brainstorming skills.
   6. Effectively express his/her research ideas and findings both orally and in writing
   7. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
6. Learning the Invariance concept and its combination with Tensors.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Acquire scientific knowledge and work independently
   4. Work effectively in multi-disciplinary research teams
   5. Develop mathematical, communicative, problem-solving, brainstorming skills.
   6. Effectively express his/her research ideas and findings both orally and in writing
   7. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
7. Observing the natural fitting of Electromagnetic Theory with Relativity Theory.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Work effectively in multi-disciplinary research teams
   6. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   7. Develop mathematical, communicative, problem-solving, brainstorming skills.
   8. Effectively express his/her research ideas and findings both orally and in writing
   9. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
8. The awareness of the short-coming of Special Relativity in the analysis of Graviatation.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Acquire scientific knowledge and work independently
   4. Work effectively in multi-disciplinary research teams
   5. Develop mathematical, communicative, problem-solving, brainstorming skills.
   6. Effectively express his/her research ideas and findings both orally and in writing

   Method of assessment

   1. Written exam
   2. Homework assignment
9. The generalization of Special Relativity to General Relativity.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Acquire scientific knowledge and work independently
   4. Work effectively in multi-disciplinary research teams
   5. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   6. Effectively express his/her research ideas and findings both orally and in writing

   Method of assessment

   1. Written exam
   2. Homework assignment
10. The basic calculational methods of Tensor Analysis

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Acquire scientific knowledge and work independently
    4. Work effectively in multi-disciplinary research teams
    5. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
11. Learning the application of Tensors in Riemannian Geometry.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    4. Acquire scientific knowledge and work independently
    5. Work effectively in multi-disciplinary research teams
    6. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    7. Develop mathematical, communicative, problem-solving, brainstorming skills.
    8. Effectively express his/her research ideas and findings both orally and in writing
    9. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
12. The learning of the application of Riemannian Geometry in General Relativity.

    Contribution to Program Outcomes

    1. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    2. Acquire scientific knowledge and work independently
    3. Work effectively in multi-disciplinary research teams
    4. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    5. Develop mathematical, communicative, problem-solving, brainstorming skills.
    6. Effectively express his/her research ideas and findings both orally and in writing
    7. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
13. Learning the analysis and solution techniques of Einstein Field Equations.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    4. Acquire scientific knowledge and work independently
    5. Work effectively in multi-disciplinary research teams
    6. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    7. Develop mathematical, communicative, problem-solving, brainstorming skills.
    8. Effectively express his/her research ideas and findings both orally and in writing
    9. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
14. Learning the frequently coincided analytıcal solutions of Einstein Field Equations and their physical interpretations.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Acquire scientific knowledge and work independently
    4. Work effectively in multi-disciplinary research teams
    5. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    6. Develop mathematical, communicative, problem-solving, brainstorming skills.
    7. Effectively express his/her research ideas and findings both orally and in writing
    8. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
15. The learning of Metric Tensors which are solutions of Einstein Field Equations and their phsical applications via Lagrange Equations.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    4. Acquire scientific knowledge and work independently
    5. Work effectively in multi-disciplinary research teams
    6. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    7. Develop mathematical, communicative, problem-solving, brainstorming skills.
    8. Effectively express his/her research ideas and findings both orally and in writing
    9. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment

Contents
Week 1:	Introduction to Classical Mechanics
Week 2:	Lagrange Function, Euler-Lagrange Equations and their application in Classical Mechanics
Week 3:	Introduction to Special Relativity
Week 4:	Lorentz Transformations and the Concept of Invariance
Week 5:	Special Relativity and Electromagnetic Theory
Week 6:	The Shortcomings of Special Relativity and need for a General Theory
Week 7:	Invariance and Tensors
Week 8:	Basic Calculations with Tensors
Week 9:	The use of Tensors in Riemannian Geometry. Midterm Exam.
Week 10:	Riemann Curvature, Ricci and Scalar Ricci Tensors.
Week 11:	Einstein Field Equations.
Week 12:	The Analytical solutions of Einstein Field Equations.
Week 13:	The applications of the Analytical solutions of Einstein Field Equations to phsical problems via Lagrange function ve Euler-Lagrange equations.
Week 14:	The Fitting of General Relativity with experimental and observational physical data and introduction to General Relativistic Cosmology and Black Holes.
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	• Ray D’Inverno, Introducing Einstein’s Relativity, Oxford University Press, 1992 • David C. Kay, Tensor Calculus, Schaum’s Outline Series, 1988 • S. Chandrasekkhar, The Mathematical Theory of Black Holes, Oxford University Press,1992 • •
Recommended readings:	J. Foster J. D. Nightingale, A Short Course in General Relativity, Second edition, Springer-Verlag, 1995 • Articles and Lecture Notes from Arxiv.org preprint server
	* 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:	9	30
Other in-term studies:		0
Project:		0
Homework:	5, 7, 12	30
Quiz:		0
Final exam:	16	40
	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:	15	3
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	22.5	1
Mid-term:	3	1
Personal studies for final exam:	30	1
Final exam:	3	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)