Partial Fractions

The course has been designed for pre -engineering students. It explains the  concept of partial fractions.

The partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator.

The concept was discovered independently in 1702 by both Johann Bernoulli and Gottfried Leibniz.

The concept of proper and improper polynomial fractions are explained in details with solved problems. It includes polynomial fractions with different types of denominators and their decomposition into simpler fractions, supplemented by solved example and assignments. Under Proper Polynomial fractions,the following cases are studied:

i)Denominator with linear nonrepeated factors

ii)Denominator with linear repeated factors

iii)Denominator with linear and irreducible quadratic factors

The prerequisite for the course with explanatory videos and assignments have also been provided. It has applications in higher  education mainly in calculus. In probability,Integrating a function to infinity can model the probability of an event as the probability approaches 100%.Integration by parts is needed in problems containing electric circuits, heat transfer,vibrations,structures, fluid mechanics,transport modelling, air pollution, and electro magnetics. Algebraic function which are difficult to differentiate can be made easier by changing them to partial fractions. In differentiation and in inverse Laplace transform also partial fraction is widely used.

Partial fractions provides algorithms for various computations with rational functions, including the explicit computation of antiderivatives,[2] Taylor series expansions, inverse Z-transforms, inverse Laplace transforms.