Category:Examples of Laplace Transforms
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This category contains examples of Laplace Transform.
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.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Examples of Laplace Transforms"
The following 37 pages are in this category, out of 37 total.
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- Laplace Transform of Constant Mapping/Examples
- Laplace Transform of Constant Mapping/Examples/Example 1
- Laplace Transform of Constant Multiple/Examples
- Laplace Transform of Constant Multiple/Examples/Example 1
- Laplace Transform of Derivative/Examples
- Laplace Transform of Derivative/Examples/Example 1
- Laplace Transform of Exponential times Function/Examples
- Laplace Transform of Exponential times Function/Examples/Example 1
- Laplace Transform of Exponential times Function/Examples/Example 2
- Laplace Transform of Exponential times Function/Examples/Example 3
- Laplace Transform of Exponential times Function/Examples/Example 4
- Laplace Transform of Exponential times Function/Examples/Example 5
- Laplace Transform of Exponential/Examples
- Laplace Transform of Exponential/Examples/2 e^4 t
- Laplace Transform of Function of t minus a/Examples
- Laplace Transform of Function of t minus a/Examples/Example 1
- Laplace Transform of Function of t minus a/Examples/Example 2
- Laplace Transform of Integral/Examples
- Laplace Transform of Integral/Examples/Example 1
- Laplace Transform/Examples
- Laplace Transform/Examples/Example 1
- Laplace Transform/Graphical Interpretation/Examples
- Laplace Transform/Graphical Interpretation/Examples/Cosine t of -3 + 12 i
- Laplace Transform/Graphical Interpretation/Examples/Cosine t of 3 - 9 i
- Laplace Transform/Graphical Interpretation/Examples/Cosine t of Half + 4 i
- Linear Combination of Laplace Transforms/Examples
- Linear Combination of Laplace Transforms/Examples/Example 1