This course will enable students to:
a) A practical approach to learning basic features of operating systems: DOS, UNIX, Windows, Linux; Graphical packages: Origin, Gnuplot; Latex and Internet.
b) C/C++ Programming: Introduction to C/C++, constants, variables, data types, declaration of variables, user defined declaration, operators, hierarchy of arithmetic operators, expressions and statements; control statements: if, switch, conditional operation, go to, if……else; Decision making and looping statements: while, do…while, for built in functions and programme structure, strings; input and output statements; pointers and arrays; sub-programmes; function overloading, recursion; file access.
Lab work:
Solving Problems related to topics covered in the course by actual Programming and obtaining results.
(a) Mathematical Operations using Mathematica (or Matlab): Running Mathematica, numerical calculations, graphics, 3 D plots, equation solving, matrices, mathematical relations, complex numbers, simplifications, algebraic expressions, mathematical operations, in built functions, differentiation, integration, series, limits.
(b) Advanced Mathematics: Procedural programming, loops, conditional programming, producing output, linking external programme, functional programming, numerical operation of data, statistical calculations, minimization, and derivatives of unknown functions.
(a) Matrices: Product of matrices, inversion using iterative methods and accessory.
Numerical Linear Algebra: Solution of system of linear equations, direct methods, error analysis.
Curve fitting: Least square fitting methods, linear regression, polynomial regression, iterative methods.
(b) Numerical differentiation and integration methods: Numerical methods for derivatives, minima and maxima of a function, numerical integration methods for one dimensional to multi-dimensional integrations using Simpson’s rule, quadrature formula and Monte Carlo methods.
(a) Interpolation: Splines, Numerical methods for ordinary and partial differential equations: Euler’s method, Range-Kutta method for ordinary differential equations; stability and convergence
(b) Partial differential equations using matrix method for difference equation, relaxation method, initial value problems, stability, convergence and qualitative properties.
Random numbers, Monte Carlo integral methods, importance of sampling, Fast Fourier Transform.
Quantum Simulations: Time-independent Schrödinger equation in one dimension (radial or linear equations); Scattering from a spherical potential, Born Approximation
Bound State Solutions: Single particle time dependent Schrödinger equation; Hartree Fock Theory: restricted and unrestricted theory applied to atoms; Schrödinger equation in a basis: Matrix operations, Variation properties; Application of basis functions to atomic, molecular and solid state calculations.