Nature, meaning and methods of computer simulation, choice and usage
of programming languages and use of graphical techniques.
Computability and algorithmic complexity, P, NP and N-Pcomplete
problems. The travelling salesman problem. Numerical methods of
solving ordinary differential equations. Simple. Multi-step and Implicit Methods, Runge-Kutta methods. Harmonic Oscillations. Damped and
Driven Oscillator. Methods of numerical integration across discontinuities.
Anharmonic, Free and Forced oscillators. Coupled oscillators. Electrical
Circuit oscillations. Chaotic behaviour in dynamical systems. Simple onedimensional
maps. Period doubling. Stability, Order and Chaos in 2dimensional
motion. Mathematical idealizations and computer models
(cellular automata) of physical systems. Wave Phenomenon. Fourier
analysis. Interference, Diffraction and Polarization. Simulation of Young's
double slit experiment. Boundary value and eigenvalue problems.
Numerov algorithm. Green function solutions. Stationary solutions of the
Schrodinger equation. Some examples. The quantum mechanical
harmonic oscillator. Graphical display of classical and wave mechanical
probability densities. Special functions and Gaussian quadratures. Some
applications. Matrix inversions. Numerical diagonalization. Reduction to
tridiagonal form. Some applications. Monte Carlo methods. Generation of
random variables having specified distribution. Metropolis algorithm.
Applications to some physical problems.
- Teacher: yiqbal Yasir Iqbal