What is the definition of the Laplace transform as described in the chapter?

The Laplace transform of a function f(t) is defined as the semi-infinite integral L{f(t)} = ∫[0,∞] e^(-st) f(t) dt, where s is a positive parameter that ensures convergence.

The Laplace transform converts a function of time, f(t), into a function of a complex variable, s. The integral runs from 0 to infinity, and the parameter s must be positive and sufficiently large for the integral to converge. In more advanced contexts, s can be complex, but the real part of s must remain positive for convergence to be guaranteed.