Difference between revisions of "Laplace Transform"
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| Line 2: | Line 2: | ||
|+ Caption text | |+ Caption text | ||
|- | |- | ||
| − | ! <math> f(t) </math> !! <math> F(s) = \mathcal{L}|f(t)| </math> | + | ! <math> f(t) </math> !! <math> F(s) = \mathcal{L}|f(t)| </math> |
|- | |- | ||
| − | | | + | | <math> 1 </math> || <math> </math> |
|- | |- | ||
| − | | | + | | <math> e^{at} </math> || <math> </math> |
|- | |- | ||
| − | | | + | | <math> t^{n} </math> || <math> </math> |
| + | |- | ||
| + | | <math> \sin{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> \cos{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> \sinh{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> \cosh{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> e^{at}\sin{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> e^{at}\cos{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> e^{at}\sinh{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> e^{at}\cosh{at} </math> || <math> </math> | ||
| + | |- | ||
| + | | <math> t^{n}e^{at} </math> || <math> </math> | ||
|} | |} | ||
==Resources== | ==Resources== | ||
* [https://tutorial.math.lamar.edu/classes/de/LaplaceIntro.aspx Laplace Transforms], Paul's Online Notes | * [https://tutorial.math.lamar.edu/classes/de/LaplaceIntro.aspx Laplace Transforms], Paul's Online Notes | ||
Revision as of 16:04, 20 September 2021
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(t) } | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(s) = \mathcal{L}|f(t)| } |
|---|---|
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^{n} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sinh{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cosh{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{at}\sin{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{at}\cos{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{at}\sinh{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{at}\cosh{at} } | |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^{n}e^{at} } |
Resources
- Laplace Transforms, Paul's Online Notes
