
# 8: Laplace Transforms


IN THIS CHAPTER we study the method of Laplace transforms, which illustrates one of the basic problem solving techniques in mathematics: transform a difﬁcult problem into an easier one, solve the latter, and then use its solution to obtain a solution of the original problem. The method discussed here transforms an initial value problem for a constant coefﬁcient equation into an algebraic equation whose solution can then be used to solve the initial value problem. In some cases this method is merely an alternative procedure for solvingproblems that can be solved equally well by methods that we considered previously; however, in other cases the method of Laplace transforms is more efﬁcient than the methods previously discussed. This is especially true in physical problems dealing with discontinuous forcing functions.