COURSE UNIT TITLE

: MATHEMATICAL METHODS IN PHYSICS - II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5125 MATHEMATICAL METHODS IN PHYSICS - II ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR 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   Using of mathematical knowledge s of special functions in physical problems
2   Being able to recognize Legendre, Bessel and Hermite differential equations and to analyze the properties of polynomials coming from their solutions and their importance in Physics
3   Being able to solve Poisson, heat and wave equations and understanding the importance of partial differential equations in Physics
4   Being able to adaptation to mathematical models of physical problems
5   Being able to using of mathematical methods for solving of physical problems
6   Being able to have the skill of using theoretical and applied knowledge for the problem solutions in the field
7   Being able to understand solution methods of solving systems of linear differential equations.
8   Being able to understand the Laplace transform method of linear differential equations.
9   Being able to understanding of the fundamental concepts of group theory
10   Being able to solve problems within group theory and describe their significance in physics

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Chapter-1: Special Functions of Mathematical Physics Legendre s equation, Reduction relations for the Legendre polynomials, Orthogonality of Legendre polynomials, The associated Legendre functions, Hermite s equation, Recurrence relations for Hermite polynomials.
2 Chapter-1: Special Functions of Mathematical Physics The orthogonal Hermite functions, Laguerre s equation, Recurrence relations for Laguerre polynomials, The orthogonal Laguerre functions, The associated Laguerre polynomials.
3 Chapter-1: Special Functions of Mathematical Physics The Rodrigues formula of associated Laguerre polynomials, Generating function for the associated Laguerre polynomials, Recurrence relations of associated Laguerre polynomials, The orthogonal associated Laguerre functions
4 Chapter-1: Special Functions of Mathematical Physics Bessel s equation, Bessel functions of the second kind Yn(x), Bessel's integral representation, Approximations to the Bessel functions, Orthogonality of Bessel functions, Spherical Bessel functions.
5 Chapter-2: The Calculation of Variations The Euler-Lagrange equation, Variational problems with constraints, Hamilton's principle and Lagrange s equation of motion, Rayleigh-Ritz method, Hamilton's principle and canonical equations of motion, The Hamilton-Jacobi equation, Variational problems.
6 1st Midterm
7 Chapter-3:The Laplace Transformation Definition of the Laplace transform(LT), Existence of the Laplace transforms, Laplace transforms of some elementary functions, Shifting theorems, The first shifting theorem, The second shifting theorem, The unit step function, LT of a periodic function.
8 Chapter-3:The Laplace Transformation Laplace transforms of derivatives, Laplace transforms of functions defined by integrals, A note on integral transformations Chapter-4 :Partial Differential Equations Linear second-order partial differential equations, Solutions of Laplace's equation: separation of variables, Solutions of the wave equation.
9 Chapter-4 :Partial Differential Equations Solution of Poisson s equation: Green s functions, Laplace transform solutions of boundary-value problems
10 2nd Midterm
11 Chapter-5:Simple Linear Integral Equations Classification of linear integral equations, Some methods of solution, Separable kernel, Neumann series solutions, Transformation of an integral equation into a differential equation, LT solution, Fourier transform solution, The Schmidt-Hilbert method of solution
12 Chapter-5:Simple Linear Integral Equations Relation between differential and integral equations, Use of integral equations, Abel's integral equation, Classical simple harmonic oscillator, Quantum simple harmonic oscillator
13 Chapter-6 : Elements of Group Theory Definition of a group (Group axioms), Cyclic groups, Group multiplication table, Isomorphic groups, Group of permutations and Cayley s theorem, Subgroups and cosets, Conjugate classes and invariant subgroups, Group representations.
14 Chapter-6 : Elements of Group Theory Some special groups, The symmetry group D2,D3, One-dimensional unitary group U(1), Orthogonal groups SO(2) and SO(3), The SU(n) groups, Homogenous Lorentz group.

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


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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 12 3 36
Preparations before/after weekly lectures 12 4 48
Preparation for midterm exam 2 6 12
Preparation for final exam 1 6 6
Preparing presentations 12 3 36
Preparing assignments 12 2 24
Midterm 2 2 4
Final 1 2 2
TOTAL WORKLOAD (hours) 168

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

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

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