Subsection B.2.3 Laplace Transform and Integration by Parts: An Analogy
When applying the Laplace Transform, think of it as a way of "unwrapping" the derivatives of a function. Just like how you can redistribute "work" between functions using integration by parts, the Laplace Transform temporarily converts a differential equation into an algebraic one, allowing you to solve it more easily.
Once the problem is solved in the transformed space, we can "repackage" the function by applying the inverse Laplace Transform, revealing the solution in its original form.
