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gptkbp:instanceOf
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gptkb:transformation
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gptkbp:application
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gptkb:probability_theory
gptkb:signal_processing
control theory
circuit analysis
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gptkbp:appliesTo
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exponentially bounded functions
piecewise continuous functions
|
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gptkbp:definedIn
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integral from 0 to infinity of f(t) e^{-st} dt
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gptkbp:domain
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complex numbers
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gptkbp:firstPublished
|
18th century
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gptkbp:generalizes
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gptkb:Fourier_Transform
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gptkbp:hasInverse
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Inverse Laplace Transform
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gptkbp:mappedFrom
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time domain
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gptkbp:mapType
|
complex frequency domain
|
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gptkbp:namedAfter
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gptkb:Pierre-Simon_Laplace
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gptkbp:notation
|
L{f(t)}
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gptkbp:property
|
gptkb:convolution_theorem
linearity
differentiation in time domain
frequency shifting
integration in time domain
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gptkbp:range
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complex numbers
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gptkbp:relatedTo
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gptkb:Fourier_transform
gptkb:Z-transform
gptkb:Mellin_transform
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gptkbp:usedFor
|
solving differential equations
|
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gptkbp:usedIn
|
gptkb:mathematics
engineering
physics
|
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gptkbp:variant
|
s
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gptkbp:bfsParent
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gptkb:David_Widder
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gptkbp:bfsLayer
|
5
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|
https://www.w3.org/2000/01/rdf-schema#label
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The Laplace Transform
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