COURSE UNIT TITLE

: MATHEMATICAL METHODS IN PHYSICS - I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5126 MATHEMATICAL METHODS IN PHYSICS - I ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR YUSUF YÜKSEL

Offered to

PHYSICS
PHYSICS

Course Objective

Mathematics is not a mediator for physics, the contrary understanding the nature and form of representation. For this reason, the science of physics has a very strong mathematical mesh. The purpose of this course, the understanding of mathematical of physics deal together with methods, to acquire to students subtle relationship between the basic mathematical formalism with the results of theoretical in the physics.

Learning Outcomes of the Course Unit

1   Being able to use vector analysis and vector algebra and make differential and integral calculus with vector operators.
2   Comprehending the importance of coordinate transformations in physics, to be able to understand linear and orthogonal transformations
3   Recognizing curved coordinate systems and to be able to analyze them with scale parameters.
4   Being able to obtain and interpret vector operators in curved coordinate systems
5   Being able to solve differential equations using power series and Frobenius methods comprehending series expansion method
6   Recognizing the general properties of determinants and matrices, to be able to make operations with them and to be able to solve eigenvalue-eigenvector problems.
7   Being able to comprehend Fourier series and coefficients, to understand their importance in physics and to analyze related problems.
8   Being able to make operations with complex numbers and to use different presentations
9   Being able to recognize complex functions and to discriminate analytical and harmonic functions
10   Being able to solve complex integrals using Cauchy theorem and integral formulas
11   Being able to solve complex and real integrals using residual theorem

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Chapter-1: Vector and Tensor Analysis Vectors and Scalars, Vector algebra, Equality of vectors, Vector addition, Multiplication by a scalar, The scalar product, The vector product, The triple scalar product, The triple vector product, Change of coordinate system, The lineer vector space, Vector differentiation, Space curves, Motion in a plane
2 Chapter-1: Vector and Tensor Analysis A vector treatment of classical orbit theory, Vector differential of a scalar field and the gradient, Conservative vector field, The vector differential operator, Vector differentiation of a vector field, Orthogonal curvilinear coordinates, Special orthogonal coordinate systems, Cylindrical-Spherical coordinates
3 Chapter-1: Vector and Tensor Analysis Vector integration and integral theorems, Helmholtz s theorem, Some useful integral relations, Tensor analysis, The line element and metric tensor, Associated tensors, Geodesics in a Riemannian space, Covariant differentiation
4 Chapter-2 : Ordinary Differential Equations First-order differential equations, Second-order equations with constant coefficients, The Euler linear equation, Solutions in power series, Simultaneous equations, Gamma and Beta Functions.
5 Chapter-3 : Matrix Algebra Definition of a matrix, Equality of matrices, Addition of matrices, Symmetric and skew-symmetric matrices, The matrix representation of a vector product, The inverse of a matrix, Complex conjugate of a matrix, Hermitian conjugation, Unitary matrix
6 Chapter-3: Matrix Algebra Rotation matrices, Trace of a matrix, Orthogonal and unitary transformations, The matrix eigenvalue problem, Diagonalization of a matrix, Eigenvectors of commuting matrices, Cayley-Hamilton theorem, Normal modes of vibrations, Direct product of matrices
7 1st Midterm
8 Chapter-4 : Fourier Series and Integrals Periodic functions, Fourier series; Euler-Fourier formulas, Gibb s phenomena, Convergence of Fourier series and Dirichlet conditions, Half-range Fourier series, Change of interval, Parseval s identity, Alternative forms of Fourier series
9 Chapter-4 : Fourier Series and Integrals Integration and differentiation of a Fourier series, Vibrating strings, RLC circuit, Multiple Fourier series, Fourier integrals and Fourier transforms, Heisenberg's uncertainty principle, Wave packets and group velocity, Heat conduction equation
10 Chapter-4 : Fourier Series and Integrals Fourier transforms for functions of several variables, The Fourier integral and the delta function, Parseval's identity for Fourier integrals, The convolution theorem for Fourier transforms, The Delta function and Green's function method
11 2nd Midterm
12 Chapter-6 : Functions Of A Complex Variable Complex numbers, Functions of a complex variable, Mapping, Branch lines and Riemann surfaces, The differential calculus of functions of a complex variable, Elementary functions of a complex variable which is z, Complex integration
13 Chapter-6 : Functions Of A Complex Variable Series representations of analytic functions, Complex series, Ratio test, Uniform convergence and the Weierstrass M-test, Power series and Taylor series, Taylor series of elementary functions, Laurent series
14 Chapter-6 : Functions Of A Complex Variable Integration by the method of residues: Residues, The residue theorem, Evaluation of real definite integrals: Improper integrals of the rational function, Fourier integrals of different forms

Recomended or Required Reading

Textbook(s):
Mathematical Methods for Physicists: A concise introduction, (Tai L. Chow Cambridge University Press 2000 )

Supplementary Book(s):
Mathematical Methods in Physical Sciences (Mary L. Boas)
Mathematical Physics (S.Hassani)
Mathematical Methods in Physics (S.D.Lindenbaum),
Introduction to Mathematical Physics (C.W.Wong).
Introduction to Ordinary Differential equations (S.L. Ross, fourth ed.)
Special Functions For Scientists and Engineers (W.W.Bell)
Special Functions (G.E Andrews,R Askey, and R. Roy)
Mathematical Methods for Physicists (G.B.Arfken, H.J.Weber, fourth ed.)

Planned Learning Activities and Teaching Methods

1.Lecturing
2.Question-Answer
3.Discussing
4.Home Work

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 RPT REPORT
2 PRS PRESENTATION
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE RPT * 0.25 + PRS * 0.25 + FIN * 0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE RPT * 0.25 + PRS * 0.25 + FIN * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

1.The homeworks will be assessed by directly adding to the mid-term scores.
2.Final examination will be evaluated by essay type examination technique

Language of Instruction

Turkish

Course Policies and Rules

1.It is obligated to continue to at least 70% of lessons.
2.Every trial to copying will be finalized with disciplinary proceedings.
3.The instructor has right to make practical quizzes. The scores obtained from quizzes will be directly added to exam scores.

Contact Details for the Lecturer(s)

ismail.sokmen@deu.edu.tr

Office Hours

The one day a week

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 4 52
Preparation for midterm exam 2 10 20
Preparation for final exam 1 10 10
Preparing assignments 13 2 26
Preparing presentations 13 3 39
Midterm 2 2 4
Final 1 2 2
TOTAL WORKLOAD (hours) 192

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.15553433
LO.25553433
LO.35553433
LO.45553433
LO.55553433
LO.65553433
LO.75553433
LO.85553433
LO.95553433
LO.105553433
LO.115553433

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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