Revision history for TutoriumMathe3Laplace
Additions:
||Verschiebungsregel (Versch. nach rechts)||f(t-a)||{{image url="Funktion19.jpg" width="80" class="center"}}
e^(-sα)F(s)||{{image url="Funktion20.jpg" width="90" class="center"}}
e^(δt)cos(ωt) ||{{image url="Funktion21.jpg" width="90" class="center"}}
(s+δ)/((s+δ)^2+ω^2)||
e^(-sα)F(s)||{{image url="Funktion20.jpg" width="90" class="center"}}
e^(δt)cos(ωt) ||{{image url="Funktion21.jpg" width="90" class="center"}}
(s+δ)/((s+δ)^2+ω^2)||
Deletions:
Additions:
||Faltungsregel||{{image url="Funktion16.jpg" width="200" class="center"}}
f(t)*g(t)*g(t)=∫f(ξ)g(t-ξ)dξ wobei ∫ von 0 bis t||F(s)* G(s)||{{image url="Funktion17.jpg" width="100" class="center"}}
e^(-δt)sin(ωt)||{{image url="Funktion18.jpg" width="100" class="center"}}
ω/((s+δ)^2+ω^2) ||
f(t)*g(t)*g(t)=∫f(ξ)g(t-ξ)dξ wobei ∫ von 0 bis t||F(s)* G(s)||{{image url="Funktion17.jpg" width="100" class="center"}}
e^(-δt)sin(ωt)||{{image url="Funktion18.jpg" width="100" class="center"}}
ω/((s+δ)^2+ω^2) ||
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Additions:
||Dämpfungsregel||{{image url="Funktion12.jpg" width="50" class="center"}}
e^(αt)f(t)||{{image url="Funktion13.jpg" width="50" class="center"}}
F(s-α)||{{image url="Funktion14.jpg" width="60" class="center"}}
cos(ωt) ||{{image url="Funktion15.jpg" width="60" class="center"}}
s/(s^2+ω^2)||
e^(αt)f(t)||{{image url="Funktion13.jpg" width="50" class="center"}}
F(s-α)||{{image url="Funktion14.jpg" width="60" class="center"}}
cos(ωt) ||{{image url="Funktion15.jpg" width="60" class="center"}}
s/(s^2+ω^2)||
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Additions:
||Integrationsregel||{{image url="Funktion8.jpg" width="80" class="center"}}
∫f(ξ)dξ wobei ∫ von 0 bis 1||{{image url="Funktion9.jpg" width="50" class="center"}}
(1/s)F(s)||{{image url="Funktion10.jpg" width="60" class="center"}}
sin(ωt) ||{{image url="Funktion11.jpg" width="60" class="center"}}
ω/(s^2+ω^2) ||
∫f(ξ)dξ wobei ∫ von 0 bis 1||{{image url="Funktion9.jpg" width="50" class="center"}}
(1/s)F(s)||{{image url="Funktion10.jpg" width="60" class="center"}}
sin(ωt) ||{{image url="Funktion11.jpg" width="60" class="center"}}
ω/(s^2+ω^2) ||
Deletions:
Additions:
||Differentationsregel (n-te) ||f^ n(t) ||{{image url="Funktion7.jpg" width="200" class="center"}}
s^nF(s)-s^(n-1)f(0)-s^(n-2)j(0)-..-sf^(n-2)(0)-f^(n-1)(0) ||t^ n ||n!/s^(n+1) ||
s^nF(s)-s^(n-1)f(0)-s^(n-2)j(0)-..-sf^(n-2)(0)-f^(n-1)(0) ||t^ n ||n!/s^(n+1) ||
Deletions:
Additions:
||Linearitätsregel ||{{image url="Funktion1.jpg" width="200" class="center"}}
λt(t)+μg(t) wobei λ,μЄR ||{{image url="Funktion2.jpg" width="100" class="center"}}
λF(s)+μG(s) ||{{image url="Funktion3.jpg" width="37" class="center"}}
e^(αt) ||{{image url="Funktion4.jpg" width="40" class="center"}}
1/(s-α) ||
||Differentationsregel (1.) ||{{image url="Funktion5.jpg" width="27" class="center"}}
f.(t)||s F(s) - f(0) ||t ||1/s² ||
||Differentationsregel (2.) ||{{image url="Funktion6.jpg" width="30" class="center"}}
f..(t)||s² F(s) - s f(0) ||t² ||2/s³ ||
λt(t)+μg(t) wobei λ,μЄR ||{{image url="Funktion2.jpg" width="100" class="center"}}
λF(s)+μG(s) ||{{image url="Funktion3.jpg" width="37" class="center"}}
e^(αt) ||{{image url="Funktion4.jpg" width="40" class="center"}}
1/(s-α) ||
||Differentationsregel (1.) ||{{image url="Funktion5.jpg" width="27" class="center"}}
f.(t)||s F(s) - f(0) ||t ||1/s² ||
||Differentationsregel (2.) ||{{image url="Funktion6.jpg" width="30" class="center"}}
f..(t)||s² F(s) - s f(0) ||t² ||2/s³ ||
Deletions:
||Differentationsregel (1.) ||{{image url="Funktion5.jpg" width="27" class="center"}}||s F(s) - f(0) ||t ||1/s² ||
||Differentationsregel (2.) ||{{image url="Funktion6.jpg" width="30" class="center"}}||s² F(s) - s f(0) ||t² ||2/s³ ||
Deletions:
Additions:
||Verschiebungsregel (Versch. nach rechts)||f(t-a)||{{image url="Funktion19.jpg" width="80" class="center"}}||{{image url="Funktion20.jpg" width="90" class="center"}} ||{{image url="Funktion21.jpg" width="90" class="center"}} ||
Deletions:
Additions:
||Verschiebungsregel (Versch. nach rechts)||f(t-a)||{{image url="Funktion19.jpg" width="50" class="center"}}||{{image url="Funktion20.jpg" width="60" class="center"}} ||{{image url="Funktion21.jpg" width="60" class="center"}} ||
Additions:
||Faltungsregel||{{image url="Funktion16.jpg" width="200" class="center"}}||F(s)* G(s)||{{image url="Funktion17.jpg" width="100" class="center"}} ||{{image url="Funktion18.jpg" width="100" class="center"}} ||
Deletions:
Additions:
||Faltungsregel||{{image url="Funktion16.jpg" width="200" class="center"}}||F(s)* G(s)||{{image url="Funktion17.jpg" width="100" class="center"}} ||{{image url="Funktion18.jpg" width="60" class="center"}} ||
Deletions:
Additions:
||Faltungsregel||{{image url="Funktion16.jpg" width="200" class="center"}}||F(s)* G(s)||{{image url="Funktion17.jpg" width="60" class="center"}} ||{{image url="Funktion18.jpg" width="60" class="center"}} ||
Deletions:
Additions:
||Faltungsregel||{{image url="Funktion16.jpg" width="50" class="center"}}||F(s)* G(s)||{{image url="Funktion17.jpg" width="60" class="center"}} ||{{image url="Funktion18.jpg" width="60" class="center"}} ||
Additions:
||Dämpfungsregel||{{image url="Funktion12.jpg" width="50" class="center"}}||{{image url="Funktion13.jpg" width="50" class="center"}}||{{image url="Funktion14.jpg" width="60" class="center"}} ||{{image url="Funktion15.jpg" width="60" class="center"}} ||
Deletions:
Additions:
||Dämpfungsregel||{{image url="Funktion12.jpg" width="80" class="center"}}||{{image url="Funktion13.jpg" width="50" class="center"}}||{{image url="Funktion14.jpg" width="60" class="center"}} ||{{image url="Funktion15.jpg" width="60" class="center"}} ||
Additions:
||Integrationsregel||{{image url="Funktion8.jpg" width="80" class="center"}}||{{image url="Funktion9.jpg" width="50" class="center"}}||{{image url="Funktion10.jpg" width="60" class="center"}} ||{{image url="Funktion11.jpg" width="60" class="center"}} ||
Deletions:
Additions:
||Integrationsregel||{{image url="Funktion8.jpg" width="80" class="center"}}||{{image url="Funktion9.jpg" width="50" class="center"}}||{{image url="Funktion10.jpg" width="37" class="center"}} ||{{image url="Funktion11.jpg" width="40" class="center"}} ||
Deletions:
Additions:
||Integrationsregel||{{image url="Funktion8.jpg" width="80" class="center"}}||{{image url="Funktion9.jpg" width="100" class="center"}}||{{image url="Funktion10.jpg" width="37" class="center"}} ||{{image url="Funktion11.jpg" width="40" class="center"}} ||
Deletions:
Additions:
||Integrationsregel||{{image url="Funktion8.jpg" width="200" class="center"}}||{{image url="Funktion9.jpg" width="100" class="center"}}||{{image url="Funktion10.jpg" width="37" class="center"}} ||{{image url="Funktion11.jpg" width="40" class="center"}} ||
Additions:
||Differentationsregel (n-te) ||f^ n(t) ||{{image url="Funktion7.jpg" width="200" class="center"}} ||t^ n ||n!/s^(n+1) ||
Deletions:
Additions:
||Differentationsregel (n-te) ||f^ n(t) ||{{image url="Funktion7.jpg" width="30" class="center"}} ||t^ n ||n!/s^(n+1) ||
Additions:
||Differentationsregel (2.) ||{{image url="Funktion6.jpg" width="30" class="center"}}||s² F(s) - s f(0) ||t² ||2/s³ ||
Deletions:
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||Differentationsregel (2.) ||{{image url="Funktion6.jpg" width="27" class="center"}}||s² F(s) - s f(0) ||t² ||2/s³ ||
Additions:
||Differentationsregel (1.) ||{{image url="Funktion5.jpg" width="27" class="center"}}||s F(s) - f(0) ||t ||1/s² ||
Deletions:
Additions:
||Differentationsregel (1.) ||{{image url="Funktion5.jpg" width="37" class="center"}}||s F(s) - f(0) ||t ||1/s² ||
Additions:
||Linearitätsregel ||{{image url="Funktion1.jpg" width="200" class="center"}} ||{{image url="Funktion2.jpg" width="100" class="center"}} ||{{image url="Funktion3.jpg" width="37" class="center"}} ||{{image url="Funktion4.jpg" width="40" class="center"}} ||
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Additions:
||Linearitätsregel ||{{image url="Funktion1.jpg" width="200" class="center"}} ||{{image url="Funktion2.jpg" width="100" class="center"}} ||{{image url="Funktion3.jpg" width="37" class="center"}} || ||
Deletions:
Additions:
||Linearitätsregel ||{{image url="Funktion1.jpg" width="200" class="center"}} ||{{image url="Funktion2.jpg" width="100" class="center"}} || || ||
Deletions:
Additions:
||Linearitätsregel ||{{image url="Funktion1.jpg" width="200" class="center"}} || || || ||
Deletions:
||Linearitätsregel ||{{image url="Funktion1.jpg" width="250" class="center"}} || || || ||
Additions:
|=| |=|Originalbereich, Zeitbereich |=|Bildbereich |=|Originalfunktion, Zeitfunktion |=|Bildfunktion||
|| ||f(t), g(t)||F (s), G (s)||1||1/s||
||Linearitätsregel ||{{image url="Funktion1.jpg" width="250" class="center"}} || || || ||
||**{{files download="Mathe3Laplace.pdf"text="PDF Dokument Laplace - Transformation"}}**||
|| ||f(t), g(t)||F (s), G (s)||1||1/s||
||Linearitätsregel ||{{image url="Funktion1.jpg" width="250" class="center"}} || || || ||
||**{{files download="Mathe3Laplace.pdf"text="PDF Dokument Laplace - Transformation"}}**||
Deletions:
||Linearitätsregel|| || || || ||
Additions:
{{files}}
**Wichtige Rechenregeln und ausgewählte Korrespondenzen der Laplace – Transformation**
|| ||Originalbereich||Bildbereich||Originalfunktion/ Zeitfunktion||Bildfunktion||
||Linearitätsregel|| || || || ||
**Wichtige Rechenregeln und ausgewählte Korrespondenzen der Laplace – Transformation**
|| ||Originalbereich||Bildbereich||Originalfunktion/ Zeitfunktion||Bildfunktion||
||Linearitätsregel|| || || || ||
Deletions:
||**{{files download="Mathe3Laplace.pdf"text="PDF Dokument Laplace - Transformation"}}**||
Additions:
||cell1||cell2||
Deletions:
Additions:
{{image url="Mathe3Laplace.jpg" width="800" class="center"}}
Deletions:
Additions:
{{image url="Mathe3Laplace.jpg" width="600" class="center"}}
||**{{files download="Mathe3Laplace.pdf"text="PDF Dokument Laplace - Transformation"}}**||
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||**{{files download="Mathe3Laplace.pdf"text="PDF Dokument Laplace - Transformation"}}**||
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