Mathematical concepts I

Fundamentals: Mathematical functions, odd and even functions, Trigonometric functions, polynomial expressions, logarithms, logarthmic functions, the exponential function, constants and variables, standard forms of straight lines and parabolic equations with graphs.

Differentiation of simple functions like xⁿ, e^x, log x, higher order derivatives, partial differentiation of first and second order, total differentiation . Maxima and minima of one variable function.

Indefinite integrals, integration of standard function, methods of integration, integration by substitution, integration by parts, integration by means of a partial fractions, definite intergrals and their properties.

Roots of quadratic equations analytically and iteratively (e.g. pH of a weak acid). Numerical methods of finding roots (Newton-Raphson, binary –bisection, e.g. pH of a weak acid not ignoring the ionization of water, volume of a van der Waals gas, equilibrium constant expressions), numerical integration (Trapezoidal and Simpson’s rule, e.g. entropy/enthalpy change from heat capacity data).

Power series, Maclaurin, Taylor series, basic concepts of probability distributions (gas kinetic theory) and mean values ; Binomial (gas kinetic theory)

Note: Calculations involving use of calculator is to be avoided