Integral transform L{f}(s) = ∫_0^∞ e^{-st} f(t) dt. Converts linear ODEs with constant coefficients into algebraic equations in s; key tool in control theory and circuit analysis.
Laplace transform
Related concepts
- Riemann integral
- Linear ODE
- Fourier transform
- Fourier transform
- Neumann series: (I − λK)⁻¹ = Σ λⁿ Kⁿ for |λ|·‖K‖ < 1
- Z-transform X(z) = Σ_n x[n] z^{-n}: discrete-time analogue of Laplace
- Z{u[n]} = z/(z−1) on |z|>1; Z(2) = 2; Z(3) = 3/2
- Z-transform (discrete signals)
- Abel integral equation (weak singular)
- Wiener-Hopf equation (half-line)
- Z-transform (Jury 1958)
- Fermi 2nd-order + 1st-order DSA: power-law spectrum from diffusion-advection FP
- Gamow 1928 Coulomb-barrier tunnelling → stellar-fusion peak