**Course Objectives: **The laboratory course is aimed at

Developing elementary programming skills in FORTRAN to enable them write short programs for performing scientific calculations.

Enabling to use graphical software for visualizing important mathematical functions and their properties through 2 D and 3 D graphs.

Introducing the basics of numerical mathematics using evaluation of functions, matrices and integrals.

**Learning Outcomes**

At the end of the course, the learners should be able to:

**Write **short simple programs in FORTRAN and be able to compile and execute them in a host of machines.

**Use **standard software tools such as MATLAB and Mathematica to** perform **algebraic and numerical calculations often required in elementary physical chemistry in the areas of quantum chemistry, spectroscopy, kinetics and thermodynamics

**Use **powerful 2D and 3D graphical packages of MATLAB and Mathematica to visualize almost any function of relevance in atomic orbitals, and probability densities in quantum chemistry and spectroscopy.

**Course Contents:**

The laboratory course is aimed at

Developing elementary programming skills in FORTRAN to enable them write short programs for performing scientific calculations

Enabling to use graphical software for visualizing important mathematical functions and their properties through 2 D and 3 D graphs

Introducing the basics of numerical mathematics using evaluation of functions, matrices and integrals.

Algebraic and numerical calculations using symbolic manipulation programs–Use of Mathematica for simple manipulations

Introduction FORTRAN 77 and FORTRAN 90 programming. Elementary exercises.

Matlab calculations and elementary programming exercises for Chemistry using algebraic programming and numerical exercises

Numerical matrix diagonalization of symmetric and hermitian matrices Numerical techniques for integration: Gauss – Hermite quadrature method

Plotting atomic orbitals and calculating simple integrals involving hydrogen and several one-electron atoms. Introduction to elementary methods in numerical differentiation and integration

Introduction to Gaussian orbitals and wave functions and their visualizations.

Orthogonalizing degenerate wave functions.

Introduction to Fourier transforms and the numerical fast Fourier transform method.

Relations between time domain and frequency domain spectra.

**Text Books:**

- William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd Edition, Cambridge University Press, Cambridge, 2007.
- Forman S. Acton, Numerical Methods that Work, Mathematical Association of USA, Washington D. C., 1990.
- Rajaraman, Computer Programming using FORTRAN 77, Prentice-Hall of India, New Delhi, 2006.
- Rajaraman, Computer Programming in FORTRAN 90 and 95, Prentice-Hall of India, New Delhi, 2006
- MATLAB and Mathematica Programming manuals supplied by IIT Madras High Performance Computing Centre, IIT Madras.