Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
FBY0004		Advanced Mathematical Methods in Physics	3/0/0	DE	Turkish	9

Course Goals	Students will specialize in advanced mathematical methods of physics and will develop solving skill of problem in high level.
Prerequisite(s)	nothing
Corequisite(s)	nothing
Special Requisite(s)	nothing
Instructor(s)	Assist. Prof. Dr. Ayşegül F. Yelkenci
Course Assistant(s)	nobody
Schedule	İKU Ataköy Campus look at the program
Office Hour(s)	Şehsuvar Zebitay,12:00-13:00, Ataköy Campus,Visiting Lecturer's Room
Teaching Methods and Techniques	Lecture and discussion.
Principle Sources	1- Spiegel, M.R. (1959). Vector Analysis and Introduction to Tensor Analysis. New York: McGraw-Hill. 2- Özemre, A.Y. (1983). Fizikte Matematik Metotlar. İstanbul: İ.Ü. Fen Fakültesi. 3- Lass, H. (1950). Vector and Tensor Analysis. New York: McGraw-Hill.
Other Sources	1- Spiegel, M.R. (1959). Vector Analysis and Introduction to Tensor Analysis. New York: McGraw-Hill. 2- Özemre, A.Y. (1983). Fizikte Matematik Metotlar. İstanbul: İ.Ü. Fen Fakültesi. 3- Lass, H. (1950). Vector and Tensor Analysis. New York: McGraw-Hill.

Course Schedules
Week	Contents	Learning Methods
1. Week	Concept of tensor, contravariant and covariant vectors, contravariant, covariant and mixed tensors
2. Week	Algebrical operations with tensors, criteria in order to be a tensor (Quotient Law).
3. Week	First order partial derivative of radius vector in curvilinear coordinates and metric tensor.
4. Week	Second order partial derivative of radius vector in curvilinear coordinates and Christoffel symbols.
5. Week	Transformation rule of the Christoffel symbols and covariant derivative of the tensor.
6. Week	Gradient, divergence, curl and laplacien in tensor form.
7. Week	Levi-Civita symbol and its applications, relative tensors, absolute tensors and tensor density.
8. Week	Physical components of tensors and ortogonal coordinates.
9. Week	Curved metric spaces and geodesics of metric space.
10. Week	Riemann-Christoffel curvature tensor and tensor analysis in Riemannien space.
11. Week	Curvature tensor and integrable space.
12. Week	Symmetry properties of the curvature tensor.
13. Week	Bianchi identitys and independent components of the curvature tensor.
14. Week	Tensors in General Theory of Relativity.
15. Week
16. Week
17. Week

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	1	40
Final Exam	1	60

Program Outcomes PO-1 To acquire the ability of deeply understanding physical concepts, by extending knowledge and experience in physics. PO-2 To be able to understand, interpret, and synthesise interdisciplinary relations. PO-3 To be able to transfer field-specific information to other work groups in written, oral, and visual ways. PO-4 To be able to identify and evaluate problems relevant to the mastering field, by using various databases and bibliographic resources. PO-5 To be able to use the theoretical and applied information which is learned within the mastering field, with the help of information technologies. PO-6 To understand the fundamentals of physics in an advanced way and to acquire the ability of problem solving. PO-7 To adopt acting in accordance with scientific ethics. PO-8 To acquire the ability of reading and writing in at least one foreign language. PO-9 To be able to follow recent developments in the mastering field of physics, by making extensive scans of the literature. PO-10 To be able to develop individual decision and creativity skills.

Learning Outcomes LO-1 Students will specialize in advanced mathematical methods of physics and will develop solving skill of problem in high level. LO-2 They evaluate critically the knowledge of the advanced mathematical methods of physics LO-3 They will have in depth information in selection and implementation of mathematical methods applicable to all issues of physics. LO-4 They will specialize in the physical interpretation of the mathematical results of solved problems by them. LO-5 They independently be able to develop appropriate solutions to high level physical problems.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10
LO 1
LO 2
LO 3
LO 4
LO 5