Laplace transform
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Laplace transforms are one of the ways of solving linear ordinary differential equations (Linear ODEs) with constant coefficients. This technique allows us to transform a Linear ODE into a linear algebraic equation.
Definition
The unilateral Laplace transform is defined by
- <math>\mathcal{L} \left\{f(t)\right\}=\int_0^{\infty} e^{-st} f(t) \,dt </math>
Given the integral converges. A necessary condition for this integral to converge is \lim_{b\to\infty} e^{-sb}f(b)=0
References
- D. Lomen and D. Lovelock, Differential Equations Graphics. Model. Data., John Wiley and Sons, Toronto, 1999.
- Laplace transform on Wolfram Mathworld