http://schulphysikwiki.de/index.php?action=history&feed=atom&title=Mathe_nach_dem_Abi 2026-04-30T13:22:45Z Versionsgeschichte dieser Seite in Schulphysikwiki MediaWiki 1.23.6 http://schulphysikwiki.de/index.php?title=Mathe_nach_dem_Abi&diff=15299&oldid=prev 2019-05-14T20:39:33Z

<p>‎<span dir="auto"><span class="autocomment">Taylorreihen</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 14. Mai 2019, 20:39 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno">Zeile 27:</td> <td colspan="2" class="diff-lineno">Zeile 27:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&#160;&#160; T f(x; a) &amp; = \sum_{n=0}^\infty&#160; \frac{f^{(n)}(a)}{n!} (x-a)^n = f(a) + f'(a) (x-a) + \frac{f''(a)}{2}(x-a)^2 + \frac{f'''(a)}{6} (x-a)^3 + \ldots</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&#160;&#160; T f(x; a) &amp; = \sum_{n=0}^\infty&#160; \frac{f^{(n)}(a)}{n!} (x-a)^n = f(a) + f'(a) (x-a) + \frac{f''(a)}{2}(x-a)^2 + \frac{f'''(a)}{6} (x-a)^3 + \ldots</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{align}&lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{align}&lt;/math&gt;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*Taylorreihen von sin, cos e^x und Wurzelfunktion berechnen, Näherungswerte berechnen und mit &quot;exakten&quot; Werten vergleichen.</ins></div></td></tr> </table>

Patrick.Nordmann http://schulphysikwiki.de/index.php?title=Mathe_nach_dem_Abi&diff=15298&oldid=prev 2019-05-14T20:38:07Z

<p>‎<span dir="auto"><span class="autocomment">Folgen und Reihen</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Version vom 14. Mai 2019, 20:38 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno">Zeile 13:</td> <td colspan="2" class="diff-lineno">Zeile 13:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Folgen und Reihen==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Folgen und Reihen==</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Hund und Frauchen: ?!</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Hund und Frauchen: ?!</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Achilles und die <del class="diffchange diffchange-inline">Schidkröte </del>([https://www.geogebra.org/m/Pn8fG5Ck Geogebra])</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Achilles und die <ins class="diffchange diffchange-inline">Schildkröte </ins>([https://www.geogebra.org/m/Pn8fG5Ck Geogebra])</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Geometrische Reihen und ihr Grenzwert &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Geometrische Reihen und ihr Grenzwert</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;\sum_{k=0}^{\infty} a_0 q^k = \frac{a_0}{1-q}&lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;\sum_{k=0}^{\infty} a_0 q^k = \frac{a_0}{1-q}&lt;/math&gt;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*Der überstehende Bücherstapel!?</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Taylorreihen===</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*Wie berechnet der Rechner/Computer sin(0,1) oder e^3,9?</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">**Nur mit + - + :</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*Geogebra:</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">**[https://www.geogebra.org/m/bhuZTaW3 Taylorreihe Autor: Sabine Drobik]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">**[https://www.geogebra.org/m/QHF34ERa Taylorreihe (r=1) Autor: Dieter Küntzer]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*&lt;math&gt;\begin{align}</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&#160; T f(x; a) &amp; = \sum_{n=0}^\infty&#160; \frac{f^{(n)}(a)}{n!} (x-a)^n = f(a) + f'(a) (x-a) + \frac{f''(a)}{2}(x-a)^2 + \frac{f'''(a)}{6} (x-a)^3 + \ldots</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">\end{align}&lt;/math&gt;</ins></div></td></tr> </table>

Patrick.Nordmann http://schulphysikwiki.de/index.php?title=Mathe_nach_dem_Abi&diff=15297&oldid=prev 2019-05-14T20:29:39Z

<p>Die Seite wurde neu angelegt: „ ==Komplexe Zahlen== *Geometrischer Zugang: **Zahlengerade: N, Z, Q, R, ? **Rechnen mit Punkten in der Ebene: + - klar *? *Algebraischer Zugang: Neue Zahlen du…“</p> <p><b>Neue Seite</b></p><div><br /> ==Komplexe Zahlen==<br /> *Geometrischer Zugang:<br /> **Zahlengerade: N, Z, Q, R, ?<br /> **Rechnen mit Punkten in der Ebene: + - klar *?<br /> *Algebraischer Zugang: Neue Zahlen durch lösen von Gleichungen:<br /> **x+5=3<br /> **x*4=3<br /> **x^2=2<br /> **x^2=-1<br /> *Geometrische Interpretation von * und : in Polarkoordinaten<br /> <br /> ==Folgen und Reihen==<br /> *Hund und Frauchen: ?!<br /> *Achilles und die Schidkröte ([https://www.geogebra.org/m/Pn8fG5Ck Geogebra])<br /> *Geometrische Reihen und ihr Grenzwert <br /> :&lt;math&gt;\sum_{k=0}^{\infty} a_0 q^k = \frac{a_0}{1-q}&lt;/math&gt;</div>

Patrick.Nordmann