Laplace Transform
An integral transform that maps a real-valued time-domain function f(t) into a complex frequency-domain function F(s).
Governing formula
L{f(t)} = F(s) = ∫₀^(∞) f(t) e^(-s t) dt
SI unit
s = σ + i ω (Complex Frequency Domain)
In depth
Extends Fourier analysis to exponentially growing or transient functions. The Laplace transform converts differential equations into algebraic linear equations incorporating initial conditions, making it the premier tool for analyzing linear electric circuits and control systems.
Examples in the real world
Solving transient current responses in RL and RLC circuits subjected to sudden step-function voltage inputs.