2.To understand the subject as tool applicable in chemical science.
6.00
Unit I:
Matrix Algebra
Matrix addition and multiplication, adjoint, transpose and inverse of matrices, special matrices (symmetric, skew-symmetric, unit, diagonal); determinants (examples from Huckel theory)
6.00
Unit II:
Differential Calculus
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.
6.00
Unit III:
Integral calculus
Integral calculus: basic rules for integration, integration by substitution, integration by parts and through partial fraction.
6.00
Unit IV:
Permutation, Probability ,Vector Algebra and Calculus
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, additional and subtraction of vectors, multiplication of vectors – scalar and vector product, vector operators – gradient, divergence and curl. (Expressions only).
6.00
Unit V:
Elementary Differential Equations
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.
References:
The Chemistry Mathematics Book; E. Steiner; Oxford University Press.
Basic Mathematics for Chemicals; Tebbutt; John Wiley and Sons.
