Matrix properties: Matrix addition and multiplication, adjoint, transpose and inverse of matrices, special matrices (symmetric, skew-symmetric, unit, diagonal), determinants (examples from Huckel theory)

Rules for differentiation, applications of differential calculus including maxima and minima (examples related to maximally populated rotational energy levels, Bohr’s radius and most probable velocity from Maxwell’s distribution etc.), partial differentiation, co-ordinate transformations.

Integral calculus:  Basic rules for integration, integration by substitution, integration by parts and through partial fraction.

Permutation and Probability: permutations and combinations, probability and probability theorems, curve-fitting (including least squares fit etc.) with a general polynomial fit.

Scalars and vectors, addition, subtraction and multiplication of vectors. Vector operators: gradient, divergence and curl. (Expressions only).

Order and degree of differential equation solution of first order and first degree linear differential equation by variable-separable, homogenous and linear equations, applications to chemical kinetics, secular equilibria, quantum chemistry etc.