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, Euler’s theorem on homogenous function, extreme points and stationary points of a function, maxima and minima of a 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. Application of integral- area under a curve (simple curve), multiple integrals- double integral, change of order of integration in double integrals, triple integarls.

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.