history "Mathe3TutoriumLambda":Projekt Einsparzähler

Revision history for Mathe3TutoriumLambda

Revision [71958]

Last edited on 2016-09-26 15:16:00 by Jorina Lossau

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y'+4y=0
λ+4=0 -> λ=-4->y=Ce^(-4x)
y(2 Strich)+2y'+y=0
λ^2+2λ+1=0
λ1/2=-1+-√(1-1)
λ1=λ2=-1 -> y=C1e^(-x)+C2xe^(-x)
y(2Strich)+4y=0
λ^2+4=0
λ^2=-4
λ1,2=0+-2j -> y=Acos(2x)+Bsin(2x)
y^5+9y^4+35y(3 Strich)+79y(2 Strich)+104y'+60y=0
λ^5+9λ^4+35λ^3+79λ^2+104λ+60=0 mit den Lösungen:
λ1=-3 einfach reell
λ2=λ3=-1doppelt reell
λ4,5=-1+-2j zueinander konjugiert komplex
y=C1e^(-3x)+C2e^(-x)+C3xe^(-x)+e^(-x)*C4cos(2x)+C5sin(2x))

Revision [71957]

Edited on 2016-09-26 14:12:00 by Jorina Lossau

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any^(n)y+...+a2y(2 Strich)+a1y'+a0y=0
anλ^n+...+a2λ^2+a1λ+a0=0
einfache reelle Lösung λ->eine Teillösung y1=C1*exp(λx)
k-fache reelle Lösung λ-> k Teillösung xj=Cj*e^(j-1)exp(λx); j=1,...,k
2 konjugiert komplexe Lösungen λ1,2=a+- jw -> y1,2=e^ax(A*cos(wx)+B*sin(wx)

Revision [59041]

Edited on 2015-09-07 18:33:00 by Jorina Lossau

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**Beispiele:**
{{image url="Lambda4.jpg" width="550" class="left"}}

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{{files}}
Beispiele:
{{image url="Lambda4.jpg" width="650" class="left"}}

Revision [59040]

Edited on 2015-09-07 18:26:04 by Jorina Lossau

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Beispiele:
{{image url="Lambda4.jpg" width="650" class="left"}}

Revision [59039]

Edited on 2015-09-07 18:23:08 by Jorina Lossau

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Die allgemeine Lösung der DGL ist die Summe aller Teillösungen.

Revision [59038]

Edited on 2015-09-07 17:57:59 by Jorina Lossau

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~~{{image url="Lambda3.jpg" width="250" class="left"}}~~

Revision [59037]

Edited on 2015-09-07 17:57:05 by Jorina Lossau

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Der Lambda-Ansatz liefert ein Polynom mit denselben Koeffizienten wie die DGL. Es hat n Lösungen, die einfach, mehrfach reell oder zumindest konjugiert komplex sein können.
{{image url="Lambda3.jpg" width="250" class="left"}}

Revision [59036]

Edited on 2015-09-07 17:52:37 by Jorina Lossau

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Revision [59035]

Edited on 2015-09-07 17:39:03 by Jorina Lossau

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**Charakteristische Gleichung:**

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~~Charakteristische Gleichung:~~

Revision [59034]

Edited on 2015-09-07 17:38:25 by Jorina Lossau

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~~{{image url="Lambda1.jpg" width="450" class="center"}}~~

Revision [59033]

Edited on 2015-09-07 17:36:43 by Jorina Lossau

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{{files}}
||Geeignet für lineare homogene DGL mit konstanten reellen Koeffizienten.
**Normalform:**
{{image url="Lambda1.jpg" width="450" class="center"}}
Charakteristische Gleichung:
||

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~~{{image url="Mathe3Lambda.jpg" width="650" class="center"}}~~

Revision [43750]

Edited on 2014-08-27 15:16:28 by Jorina Lossau

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~~{{image url="Mathe3Lambda.jpg" width="600" class="center"}}~~

Revision [43749]

Edited on 2014-08-27 15:16:11 by Jorina Lossau

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||**{{files download="Mathe3Lambda.pdf"text="PDF Dokument Lambda - Ansatz"}}**||

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{{files}}
||**{{files download="Mathe3A1.pdf"text="PDF Dokument Lambda - Ansatz"}}**||

Revision [43748]

The oldest known version of this page was created on 2014-08-27 15:15:03 by Jorina Lossau