Diff. Eq. - The Laplace Transform

Chapter 8 - Laplace transforms

Laplace transforms are a tool for solving initial value problems where the differential equation is linear and has constant coefficients. 

The idea is to transform the differential equation into an algebraic equation whose solution is easier to obtain and then apply the inverse transform to solve the differential equation.

f(t)  →  F(s)

*f(t) being the original function

*F(s) representing a Laplace transform

There are two ways to represent this equation:

... or,

*ℒ - Laplace transform

The Laplace transform ℒ is a linear in the sense that ℒ[C1f1 + C2f2] = C1ℒ[f1] + C1ℒ[f2], where C1, C2 are constants.

Some more theory & example problems:

> Laplace Proofing #1

> Example 8.6

> Example 8.2

> Example 8.3