Page 36 - CatalogNEP-PS

UNIT 2 (15 Hours)

Frobenius Method and Special Functions:Singular Points of Second Order Linear Differential
Equations and their importance.Frobenius method and its applications to differential
equations.Legendre, Bessel, Hermite and Laguerre Differential Equations. Properties of Legendre
Polynomials: Rodrigues Formula, Generating Function, Orthogonality. Simple recurrence
relations.Expansion of function in a series of Legendre Polynomials.
Bessel Functions of the First Kind: Generating Function, simple recurrence relations. Zeros of
Bessel Functions and Orthogonality.
Partial Differential Equations:Solutions to partial differential equations, usingseparation of
variables: Laplace's Equation in problems of rectangular, cylindrical and spherical symmetry.
Wave equation and its solution forvibrational modes of a stretched string, rectangular and circular
membranes
Elements of complex analysis, analytic functions; Taylor & Laurent series; poles, residues and
evaluation of integrals. Elementary probability theory, random variables, binomial, Poisson and
normal distributions. Central limit theorem.

UNIT 3 (15 Hours)
Regression: Algorithm for Least square fitting of a straight line, Fitting a Power function,and
Exponential Function using conversion to linear relation by transforming the variables.Solution of
Ordinary Differential Equations: First Order ODE‘s: solution of Initial Valueproblems: (1) Euler‘s
Method and (2) Runge Kutta methods
Random Processes and Monte-Carlo Methods: Random number generation-uniform and non-
uniform distributions;Monte Carlo Integration- Hit and miss, Sample mean integration,
Metropolis Method;Computer ―Experiments‖ - applications of Monte-Carlo methods toproblems
in physics;Variational Monte-Carlo tecnique: Application to solving for the ground state of
quantum mechanical systems in 1D and 2D
Fast Fourier Transforms and Spectral Methods:Discrete Fourier Transform,Fast Fourier
Transform,SandeTukey Algorithm, Pseudospectral technique to solve the Schroedinger equation

* Tutorial(15 Hours) one hour per week

SUGGUESTED READINGS:

1. G. Arfken: Mathematical Methods for Physicist 4th edition (Academic Press).
2. J. Mathews and R. L. Walker: Mathematical Methods of Physics (I. B. House Pvt.Ltd.).
3. C. Harper: Introduction to Mathematical Physics (Prentice Hall of India).
4. A. W. Joshi: Vectors & Tensors (Wiley Eastern Limited).
5. A. W. Joshi: Elements of Group Theory (Wiley Eastern).
6. Riley, Hobson & Bence: Mathematical Methods for Physics and Engineering (Cambridge
University Press)
7. Introduction to Numerical Analysis, S. S. Sastry, 5th Edition, PHI Learning Pvt. Ltd, 2012
8. Computational Physics, Darren Walker, 1st Edition, Scientific International Pvt. Ltd, 2015
9. Applied numerical analysis, Cutis F. Gerald and P. O. Wheatley, Pearson Education, 2007
10. An Introduction to Computational Physics, T. Pang, Cambridge University Press, 2010
11. Numerical Recipes: The art of scientific computing, William H. Press, Saul A. Teukolsky
and William Vetterling, Cambridge University Press, 3rd Edition, 2007
12. Computational Problems for Physics, R. H. Landau and M. J. Páez, CRC Press, 2018

Phys.322 Electronics- II 3+1

LEARNING OBJECTIVES:

The primary objective of this course is to:

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