Mathematical concepts I

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

Differentiation of simple functions like xⁿ, e^x, logx, higher order derivatives, partial differentiation, partial differential coefficient, second order partial derivatives, total differential coefficient. 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.