1Introduction to the Matlab programming language; Operations in Matlab: basic mathematical operations with matrices & arrays
2Plotting with Matlab: line plots, 1-D, 2-D, 3-D, meshgrid, labeling axes, legends, importing and plotting data files in Matlab, Learning to use if, while, elseif commands; Simple animations
3Numerical methods for Solving Ordinary Differential Equations (ODEs); Programming in Matlab to solve 1st order and 2nd order ODEs; Solving ODEs using inbuilt matlab solvers
4The Newton Raphson method for root finding; Programming in Matlab to find roots using Newton Raphson method; Using direct matlab solvers for root finding
5Numerical methods for Integration – Rectangular Method; Trapezoidal and Simpson’s method; Programming in Matlab for integration using the above methods
6Curve Fitting Specific examples: Classical Mechanics: Newton's laws, Projectile Motion, Simple Harmonic Oscillator, Damped & Driven Harmonic Oscillator, Van der Pol Oscillator, Lorenz Equations, 1D cellular automata, Simple Fractals; etc; Quantum mechanics; Particle in a box: 1D, 2D; Energy levels & density of states; Schrödinger equation for simple quantum systems; Plotting & visualisation of various potentials; Radioactive Decay, wave packet dynamics: