Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
4PHYS266MATHEMATICAL METHODS OF PHYSICS4+046

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program PHYSICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course The aim of the course is to strengthen the mathematical background in physics.
Course Content The parts of the essential mathematical background that is necessary in undergraduate physics education and that are not studied in the basic mathematics courses will be taught.. The following topic will be covered: Basic complex calculus, Fourier series, Dirac delta function, Fourier transform, partial differential equations of physics: separation of variable method, power series solutions of differential equations. Legendre polynomials; spherical harmonics. Bessel functions. Laguerre polynomials, Hermite polynomials, gamma and beta functions.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. RECA─░ ERDEM
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources . Basic complex Analysis, J.E. Marsden (W.H. Freeman and Company,1973, San Francisco)
. Mathematics for Physicists, S.M. Lea, (Brooks/Cole- Thomson, 2004, USA)
Complex variables and applications, R.V. Churchill Donald H. Perkins, (McGraw-Hill, 1990, New York)
Mathematical methods for physicist: a concise introduction, T.L. Chow, (Cambridge University Press, 2000, New York)
Mathematical Methods for Physics and Engineer K.F. Riley, M.P. Hobson, S.J. Bence

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 10 % 5
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 45
Total
13
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 14 4 56
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 14 6 84
Application (Homework, Reading, Self Study etc.) 5 2 10
Exams and Exam Preparations 3 10 30
Total Work Load   Number of ECTS Credits 6 180

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand basic properties of complex numbers and their uses, and convert a complex quantity written in Cartesian form into polar form and vice versa.
2 To understand the meaning of a complex function and their differentiability.
3 To be bale to evaluate integrals on a complex plane.
4 To learn Residue theorem and how to evaluate some real integrals by using the methods of complex calculus.
5 To learn the notion of partial differential equations and the technique of separation variables method.
6 To learn Fourier series and their basic sues in physics, and the notion of a more generalized notion of vector spaces.
7 To learn Dirac delta function and its basic uses in physics.
8 To learn Fourier transform method and its basic usage in physics.
9 To have a general knowledge about Sturm Liouville theory and the notions of vector spaces in the space of functions and the notion of eigenfunctions
10 To be acquainted with some special functions as specific cases of Sturm-Liouville problem.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Complex numbers and functions of complex variables
2 Analyticity and differentiability of complex functions
3 Complex integrals and Cauchy Theorem
4 Singularities, Laurent expansion, poles and residues
5 Residue Theorem and its application to integrals over real numbers.
6 Partial diffrential equations in physics
7 Partial diffrential equations in physics
8 Fourier Series, Fourier transform, Dirac delta function
9 Fourier Series, Applications of Fourier transform
10 Fourier Series, Applications of Fourier transform
11 Special functions: Gama and beta functions, and their asymptotic expansion
12 Special functions
13 Series solution to diffrential equations(Legendre, Bessel functions, Laguerre polynomials)
14 Calculus of variations


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
C1 5 5 2 1 5 1 2 3 2 1
C2 5 5 2 1 5 1 2 3 2 1
C3 5 5 2 1 5 1 2 3 2 1
C4 5 5 2 1 5 1 2 3 2 1
C5 5 5 2 1 5 1 2 3 2 1
C6 5 5 3 1 5 1 2 3 2 1
C7 5 5 2 1 5 1 2 3 2 1
C8 5 5 3 1 5 1 2 3 2 1
C9 5 5 2 1 5 1 2 3 2 1
C10 5 5 3 1 5 1 2 3 2 1

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=261927&lang=en