KUK - LMS

Syllabus

MODULE NO / UNIT	COURSE SYLLABUS CONTENTS OF MODULE	NOTES
Course Code: PHY 404A Course Name: Computational Physics-II
1	Differentiation and Integration (12 hrs.) Differentiation: Taylor series method, Numerical differentiation using Newton’s forward difference formula, Backward difference formula, Stirling’s formula, Cubic splines method, Drawbacks of numerical differentiation, Integration: Trapezoidal rule, Trapezoidal rule from Lagrange linear interpolation, Simpson’s 1/3 rule, Simpson’s 3/8th rule, error in integration (Simpson and Trapezoidal), Gaussian Quadrature, Legendre–Gauss Quadrature, Numerical double integration, Numerical integration of singular integrals, Debye model.
2	Solution of Differential Equations (12 hrs.) Numerical solution of ordinary differential equations: Single step method, multi-step method, Taylor’s series method, Euler’s method, Modified Euler’s method, Fourth-order Runge Kutta method, Cubic splines method; Second order differential equations: Initial and boundary value problems, Numeric solution of radial Schrodinger equation for Hydrogen atom using Fourth-order Runge-Kutta method (when eigenvalue is given), Numerical Solutions of Partial Differential Equations using Finite Difference Method, Stability of numerical methods.
3	Random Numbers and Chaos (12 hrs.) Random numbers: Random sequences, Random number generators, Seeding, Mid-square methods, Multiplicative congruential method, Mixed multiplicative congruential methods, Modeling radioactive decay. Hit and miss Monte-Carlo methods, Monte-Carlo calculation of π, Monte-Carlo evaluation of integration, Evaluation of multidimensional integrals; Chaotic dynamics: Some definitions, The simple pendulum, Potential energy of a dynamical system. Portraits in phase space: Undamped motion, Damped motion, Driven and damped oscillator. Elementary probability theory, Binomial, Poisson and normal distributions, Central limit theorem.
4	Simulation of selected physics problems (12 hrs.) Algorithms and programs to simulate interference and diffraction of light, Simulation of charging and discharging of a capacitor, current in LR and LCR circuits, Computer models of LR and LCR circuits driven by sine and square functions, Computer model of Rutherford scattering experiment, Simulation of electron orbit in H2 ion.