Laplace transforms of common functions

Table 3.1 gives further Laplace transforms of common functions (called Laplace transform pairs). 

First, the applied time-dependent stimulus (one-shot or repetitive — voltage or current) is mapped into the complex-frequency domain, that is, the s-plane. Then, by using the s-plane versions of the impedances, we can transform the entire circuit into the s-plane. To this transformed circuit we apply the s-plane versions of the basic electrical laws and thereby analyze the circuit. We will then need to solve the resultant (transformed) differential equation (now in terms of, v rather than t). But as mentioned, we will be happy to discover that the manipulation and solution of such differential equations is much easier to do in the s-plane than in the time domain. In addition, there are also several lookup tables for the Laplace transforms of common functions available, to help along the way. We will thus get the response of the circuit in the frequency domain. Thereafter, if so desired, we can use the... 

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