ABSTRACT
Many engineering and technology problems may be represented as integro-differential equations that need to be solved. Depending on the order of the equation, the solution may be simple or very complex, especially where the standard techniques of integral and differential calculus are used. An alternative is to use the Laplace transform. The Laplace transform, L{f(t)} = F(s), is a linear operation. Therefore, if two time functions, f(t) and g(t), have Laplace transforms, then the transform of the algebraic sum of the time functions is the algebraic sum of the two separate Laplace transforms. The partial fractions technique is a means of separating out the various components of a Laplace transform expression, and transforming each term back to the time domain. This technique exploits the fact that the Laplace transform is a linear operation, and as such, the sum of the individual terms will be the overall result.
