How is the Laplace transform used in circuit analysis?

The Laplace transform converts time-domain differential equations into algebraic s-domain equations, greatly simplifying transient analysis. Components transform to impedances: R stays R, L becomes sL, C becomes 1/sC. Initial conditions appear as additional sources. After solving in s-domain, inverse Laplace transform yields time-domain response. This technique handles any input waveform, easily incorporates initial conditions, and directly reveals system poles and zeros for stability analysis.