Startseite
Forum
Fragen
Suchen
Formeleditor
Über Uns
Registrieren
Login
FAQ
Suchen
Foren-Übersicht
->
Quantenphysik
Antwort schreiben
Benutzername
(du bist
nicht
eingeloggt!)
Titel
Nachrichtentext
Smilies
Weitere Smilies ansehen
Schriftfarbe:
Standard
Dunkelrot
Rot
Orange
Braun
Gelb
Grün
Oliv
Cyan
Blau
Dunkelblau
Indigo
Violett
Weiß
Schwarz
Schriftgröße:
Schriftgröße
Winzig
Klein
Normal
Groß
Riesig
Tags schließen
Schreibt eure Formeln hier im Board am besten mit Latex!
So gehts:
Latex-Kurzbeschreibung
|
Formeleditor
[quote="caro_b"]merci für die schnelle Antwort also [latex] e^{\frac{\partial f(x)}{\partial x}}= f(x+1) [/latex][/quote]
Optionen
HTML ist
aus
BBCode
ist
an
Smilies sind
an
BBCode in diesem Beitrag deaktivieren
Smilies in diesem Beitrag deaktivieren
Spamschutz
Text aus Bild eingeben
Alle Zeiten sind GMT + 1 Stunde
Gehe zu:
Forum auswählen
Themenbereiche
----------------
Mechanik
Elektrik
Quantenphysik
Astronomie
Wärmelehre
Optik
Sonstiges
FAQ
Sonstiges
----------------
Off-Topic
Ankündigungen
Thema-Überblick
<table border="0" cellpadding="3" cellspacing="1" width="100%" class="forumline"> <tr> <th class="thCornerL" width="22%" height="26">Autor</th> <th class="thCornerR">Nachricht</th> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 16:50<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">dann vielen Dank für eure Hilfe :-)</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 16:41<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>caro_b hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote"> <br />darf ich jetzt einfach x_0 =x setzten? <br />wenn ja warum?</td> </tr></table><span class="postbody"> <br />Du darfst ja die Funktion f(x+1) um jeden Punkt entwickeln den Du willst, insbesondere auch x_0=x. <br />(Bei f und f' ist bei Dir im Argument noch ein +1 zuviel.)</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 16:06<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">und das Stillschweigen zu a - c interpretier ich mal als leise Zustimmung</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:57<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">also ich finde es auch nicht hilfreich! <br /> <br />den Operator habe ich verstanden (denke ich) <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\partial x}f(x) = \sum\limits_{k=0}^\infty \frac{(\partial x)^k}{k!} f(x) =f(x)+f''(x) +\frac{f'''}{2}+\frac{f''''}{6}...= \sum\limits_{k=0}^\infty \frac{f^k(x)}{k!} <br />"> <br /> <br />und mit dem Hinweis auf Taylor <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />T(f(x+1),x_0) <br />= f(x_0 +1) + f'(x_0 +1) (x+1-x_0) +\frac{f''(x_0)(x+1-x_0)}{2}... <br />=\sum\limits_{k=0}^\infty \frac{f^k(x_0)(x+1-x_0)^k}{k!} <br />"> <br /> <br />darf ich jetzt einfach x_0 =x setzten? <br />wenn ja warum?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:39<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ok</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>index_razor</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:36<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ich wollte nur sicherstellen, <span style="font-style: italic">daß</span> es diskutiert wird. Ob vorher oder nachher, ist mir egal.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:33<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Finde ich schon. <br /> <br />Ja, die Aufgabe ist nicht präzise gestellt. Aber das kann man diskutieren, <span style="font-style: italic">nachdem</span> die Aufgabe so diskutiert und gelöst wurden, wie vom Aufgabensteller vorgesehen.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>index_razor</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:28<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Finde ich nicht. Daß die Aufgabe eigentlich falsch gestellt ist, sollte jemandem, der versucht sie zu beantworten, klar gemacht werden. Scheinbeweise für falsche Behauptungen zu finden, ist nämlich keine Kunst.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:25<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Das ist zwar richtig, aber wenig hilfreich im Zusammenhang mit dieser Aufgabe.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>index_razor</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:19<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ein Gegenbeispiel (von Cauchy) zur Behauptung d) ist die Funktion <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?F(x) = \exp(-1/x^2)"> für <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?x\neq 0"> und <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?F(0) = 0."> <br /> <br />Für diese gilt <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?e^{\partial_x}F|_{x=0} = 0 \neq F(1)."> <br /> <br />Nicht jede Funktion wird durch ihre Taylorreihe dargestellt, selbst wenn diese existiert und konvergiert.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:13<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">der operator ist e^partial angewendet auf f(x)=x.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:12<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">der Operator ist also nicht <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />\partial x <br />"> <br />sondern <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\partial x} <br />"> <br />?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:07<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Nein, das ist Quatsch. <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br /> <br />e^\partial x=\sum\limits_{k=0}^\infty \frac{\partial^k}{k!} x = x + 1 <br />"> <br />Weil ab der zweiten Ableitung der Rest der Reiche verschwindet.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 15:01<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">also erstmal nur um zu verstehen, was das macht: <br />Beispiel: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br /> <br />f(x) = x <br /> <br />e^{\frac{\partial}{\partial x}}f(x) <br />=e^{\frac{\partial}{\partial x}}x <br />=e^{\frac{\partial}{\partial x}} <br />"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:57<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\exp[\partial_x]\, f(x)"> <br /> <br />ist definiert mittels der Taylorentwicklung der e-Funktion. Damit folgt die ganz normale Taylorentwicklung von f(x).</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:56<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>caro_b hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>jh8979 hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>caro_b hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote">merci für die schnelle Antwort <br /> <br />also <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\frac{\partial f(x)}{\partial x}}= f(x+1) <br />"></td> </tr></table><span class="postbody"> <br />Fast: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\frac{\partial}{\partial x}}f(x)= f(x+1) <br />"></td> </tr></table><span class="postbody"> <br /> <br />was leite ich denn dann da partiel nach x ab??????? <br />ich checks nicht</td> </tr></table><span class="postbody"> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{\partial}{\partial x}"> kann als Operatr aufgefasst werden, der alles ableitet was rechts von ihm steht. Jetzt setzt Du das in die Definition von e^D ein und guckst was passiert.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:54<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>jh8979 hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>caro_b hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote">merci für die schnelle Antwort <br /> <br />also <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\frac{\partial f(x)}{\partial x}}= f(x+1) <br />"></td> </tr></table><span class="postbody"> <br />Fast: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\frac{\partial}{\partial x}}f(x)= f(x+1) <br />"></td> </tr></table><span class="postbody"> <br /> <br />was leite ich denn dann da partiel nach x ab??????? <br />ich checks nicht</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:53<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>caro_b hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote">da reicht ja schon f(x) =x als gegenbeispiel, um zuzeigen, dass es nicht so ist... <br /> <br />das wird es also wohl doch nicht sein</td> </tr></table><span class="postbody"> <br />Wenn Du es richtig aufschreibst ist f(x)=x im Gegenteil ein sehr schoenes Beispiel, dass es so ist.<img src="images/smiles/balloon.gif" alt="smile" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:52<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">da reicht ja schon f(x) =x als gegenbeispiel, um zuzeigen, dass es nicht so ist... <br /> <br />das wird es also wohl doch nicht sein</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:52<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>caro_b hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote">merci für die schnelle Antwort <br /> <br />also <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\frac{\partial f(x)}{\partial x}}= f(x+1) <br />"></td> </tr></table><span class="postbody"> <br />Fast: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\frac{\partial}{\partial x}}f(x)= f(x+1) <br />"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:50<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">merci für die schnelle Antwort <br /> <br />also <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php? <br />e^{\frac{\partial f(x)}{\partial x}}= f(x+1) <br />"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>jh8979</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:46<span class="gen"> </span> Titel: Re: Operatoren</span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>caro_b hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote"> <br />zu d <br />??? <br />was ist denn genau die Funktion auf die ich D anwende?</td> </tr></table><span class="postbody"> <br />Irgendein f(x). Du musst zeigen, dass e^D genau dieselbe Wirkung hat wie T_1.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>caro_b</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 02. Nov 2019 14:33<span class="gen"> </span> Titel: Operatoren</span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><span style="font-weight: bold">Meine Frage:</span><br />Hallo,<br />es geht zwar mehr um Mathe, da wir das in der Ex3 machen, poste ich es dennoch hier.<br /><br />Aufgabe:<br />Der Laplace-Transformationsoperator L, der Translationsoperator T_h und die Exponentialfunktion eines beliebigen Operators A werden definiert als<br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?<br />F(y)=L(f(x)) = \int_0^\infty e^{-yx} f(x) \dd x <br />T_hf(x) = f(x+h)<br />e^A=\sum\limits_{k=0}^\infty \frac{A^k}{k!} <br />"><br />a) ist L linear?<br />b) F(y) = L{f(x)} mit f(x) = 1<br />c) Berechnen Sie <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?Le^{ax}"> mit y > a<br />d) Zeigen Sie, dass <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?e^D=T_1 \text{ist, mit} D=\partial_x"><br /><br /><span style="font-weight: bold">Meine Ideen:</span><br />zu a)<br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?<br />aF(y)=aL(f(x)) = a\int_0^\infty e^{-yx} f(x) \dd x<br />=\int_0^\infty e^{-yx} af(x) \dd x = L(af(x))<br /><br />F(y) + G(y) = \int_0^\infty e^{-yx} f(x) \dd x +\int_0^\infty e^{-yx} g(x) \dd x<br />=\int_0^\infty e^{-yx}[ f(x)+g(x)] \dd x<br />=L(f(x)+g(x))<br /><br />"><br /><br />damit Linearität gezeigt<br /><br />zu b)<br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?F(y)=\frac{1}{y}"><br /><br />zu c<br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?F(y)=\frac{1}{y-a}"><br /><br />zu d<br />???<br />was ist denn genau die Funktion auf die ich D anwende?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> </table>
Registrieren
Login
FAQ
Suchen
