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
FIZ 2906 MATHEMATICAL METHODS IN PHYSICS II COMPULSORY 4 2 0 8

Offered By

Physics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR EROL VATANSEVER

Offered to

Physics

Course Objective

This lecture is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the reader has an adequate preparation in general physics and calculus.

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, Being able to using of mathematical methods for solving of physical problems
5   Being able to have the skill of using theoretical and applied knowledge for the problem solutions in the field
6   Being able to understand solution methods of solving systems of linear differential equations, Being able to understand the Laplace transform method of linear differential equations.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Special Functions of Mathematical Physics The Gamma and Beta functions Special Functions of Mathematical Physics Legendre s equation,Legendre s polynomials, Rodrigues formula for Pn(x), The generating function for Pn(x), Orthogonality of Legendre polynomials
2 (Continue): Special Functions of Mathematical Physics The associated Legendre functions, Orthogonality of associated Legendre functions Hermite s equation, Rodrigues formula for Hermite polynomials Hn(x), Recurrence relations for Hermite polynomials, Generating function for the Hn(x), The orthogonal Hermite functions
3 (Continue):Special Functions of Mathematical Physics Laguerre s equation, The generating function for the Laguerre polynomials Ln(x), The orthogonal Laguerre functions The associated Laguerre polynomials, Generating function for the associated Laguerre polynomials, Associated Laguerre function of integral order
4 (Continue):Special Functions of Mathematical Physics Bessel s equation, Bessel functions of the second kind Yn(x), Hanging flexible chain, Generating function for Jn(x), Bessel s integral representation, Recurrence formulas for Jn(x) Approximations to the Bessel functions, Orthogonality of Bessel functions, Spherical Bessel functions, Sturm-Liouville systems
5 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
6 (Continue): The Calculation of Variations The modified Hamilton s principle and the Hamilton-Jacobi equation, Variational problems with several independent variables
7 Midterm exam The Laplace Transformation Definition of the Laplace transform, Existence of the Laplace transforms, Laplace transforms of some elementary functions
8 (Continue):The Laplace Transformation Shifting (or translation) theorems, The first shifting theorem, The second shifting theorem, The unit step function, Laplace transform of a periodic function Laplace transforms of derivatives, Laplace transforms of functions defined by integrals, A note on integral transformations
9 Partial Differential Equations Linear second-order partial differential equations, Solutions of Laplace s equation: separation of variables, Solutions of the wave equation: separation of variables
10 (Continue):Partial Differential Equations Solution of Poisson s equation: Green s functions, Laplace transform solutions of boundary-value problems
11 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, Laplace transform solution, Fourier transform solution, The Schmidt-Hilbert method of solution
12 (Continue):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 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 Continue): 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. Cooperative Learning
3.Question-Answer
4.Discussing
5.Home Work

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.30 + ASG * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.30 + RST * 0.40


*** 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)

erol.vatansever@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Tutorials 13 2 26
Preparations before/after weekly lectures 13 3 39
Preparing assignments 13 3 39
Preparation for midterm exam 1 12 12
Preparation for final exam 1 16 16
Midterm 1 2 2
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.10PO.11PO.12PO.13PO.14
LO.154412312211111
LO.254412312211111
LO.354412312211111
LO.454412312211111
LO.554412312211111
LO.654412312211111

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

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