Category:Definitions/Laplace Transforms
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This category contains definitions related to Laplace Transforms.
Related results can be found in Category:Laplace Transforms.
Let $f: \R_{\ge 0} \to \mathbb F$ be a function of a real variable $t$, where $\mathbb F \in \set {\R, \C}$.
The Laplace transform of $f$, denoted $\laptrans f$ or $F$, is defined as:
- $\ds \laptrans {\map f t} = \map F s = \int_0^{\to +\infty} e^{-s t} \map f t \rd t$
whenever this improper integral converges.
If this improper integral does not converge, then $\laptrans {\map f t}$ does not exist.
Pages in category "Definitions/Laplace Transforms"
The following 11 pages are in this category, out of 11 total.
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- Definition:Laplace Transform
- Definition:Laplace Transform/Also see
- Definition:Laplace Transform/Applications in Physics
- Definition:Laplace Transform/Discontinuity at Zero
- Definition:Laplace Transform/Graphical Interpretation
- Definition:Laplace Transform/Notation
- Definition:Laplace Transform/Restriction to Reals
- Definition:Laplace Transform/Technical Note