Mathematical concepts I

Fundamentals: Mathematical functions, odd and even functions, Trigonometric functions, polynomial expressions, logarithms, the exponential function, units of a measurement, interconversion of units, constants and variables, equation of a straight line in different forms and their graphs.
 

Uncertainty in experimental techniques: Displaying uncertainties, measurements in chemistry, decimal places, significant figures, combining quantities.
Uncertainty in measurement: types of uncertainties, combining uncertainties. Statistical treatment. Mean, standard deviation, relative error. Data reduction and the propagation of errors.

The tangent line and the derivative of a function),higher order derivatives, stationary points, maximum- minimum problems, inflexion points, partial differentiation, Euler’s theorem, The process of integration,  indefinite integrals, standard integrals, methods of integration (e.g. integrated rate law for second order reaction), integration by parts, definite intergrals.
 

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.