Dr. Aniruddha Chakraborty

Course Details:

The aim of the course is to give the techniques and skills of mathematics to students to be prepared for their advanced classes of quantum chemistry, molecular simulation, group theory etc.. Especially for the students of Physical Chemistry & certain areas of Inorganic Chemistry, the knowledge of Mathematics is essential to understand & interpret scientific data & mathematical expressions.  This course will cover the topics of Linear Algebra, Differential and Integral calculus, Analytical Geometry and data Analysis. This course is the pre-requisite course for quantum chemistry and group theory. The mathematical course content will be taught in conjunction with the advanced concept of physical chemistry outlined here as applications.

Module 1: Linear Algebra                                                   

Scalars & Vectors: vector, a summary of vectors & representation of 3-D co-ordinates, vector products, vector spaces, orthonormal basis set, vector functions, differentiation & integration of vector functions, gradient, divergence & Curl, line integral, surface integral, volume integrals, linear independence, basis, curvilinear coordinates, Laplacian, Green's theorem, Stokes theorem, Tensors. Matrix Algebra: Matrices & determinants, rank, matrix algebra, diagonalization, matrix property, matrix functions, eigen values, eigen vectors. Applications: Visualization in quantum chemistry, symmetry & group theory, spectroscopy.

Module 2: Calculus                                                                 

Functions, variables, Bessel functions, basic rules of differentiation, maxima & minima, exact & inexact differential, partial differentiation, limits, rules of integration, definite & indefinite integrals, first & second order differential equations, linear homogeneous/inhomogeneous equations, general solution & particular solution, polynomials, Taylor & McLaurin series, Fourier series & Fourier transforms, power series method. Applications: Kinetics, Quantum Chemistry.

Module 3: Analytical geometry and Data Analysis

Analytical geometry: Properties of different graphs & plotting of them, understanding of any kind of scientific equation - plotting of them & interpreting the physical significance of the plot, relevant especially for thermodynamic, kinetic & radioactive study, general application in all fields of chemistry. Data Analysis: Data plotting, least square fitting, concept of floating points, interpolation, asymptotic analysis, error analysis, random numbers & correlations.

References:

• Mathematics for Chemists, Charles L. Perrin, Wiley-Interscience.
• The Chemical Maths Book, E. Steiner, Oxford University Press.
• Maths for Chemists, Volumes 1 and 2, Martin C. R. Cockett and Graham Doggett, Royal Society of Chemistry, Cambridge (2003).