4.1 Definition of the Laplace Transform

4.2 Inverse Transforms and Transforms of Derivatives

4.3 Translation Theorems

4.4 Additional Operational Properties

4.5 Dirac Delta Function

4.6 Systems of Linear Differential Equations

Chapter 4 in Review

In Chapter 3 we solved linear mathematical models such as mx″ + βx′ + κx = f(t) and Lq″ + Rq′ + q/C = E(t) where the driving functions f(t) and E(t) were continuous. However, in practice, discontinuous driving functions are not uncommon. Although we solved piecewise linear DEs in Chapter 2, the Laplace transform discussed in this chapter is an especially valuable tool that simplifies the solution of such equations.