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				<div style="text-align:left;margin-bottom:20px;">  		</div><span itemprop="name" class="title">Mathematik für Ingenieure 1 für Dummies<br></span><p>Autoren:<br><span itemprop="author" class="author"><b>J. Michael Fried</b></span></p><p>Verlag:<br><b itemprop="publisher">Wiley VCH Verlag </b>&nbsp;&nbsp;<a onclick="SearchPublEnt(745)" href="#">Weitere Titel dieses Verlages anzeigen</a></p>		
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<span class="notbold">Auflage: </span>2. erweiterte und verbesserte Auflage.<br><span class="notbold">Erschienen: </span>Dezember 2013<br><span class="notbold">Seiten: </span>387<br><span class="notbold">Sprache: </span>Deutsch<br><span class="notbold">Preis: </span>19.99 €<br>
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						<div class="right-td"><span class="notbold">Ma&szlig;e: </span>241x177x25<br><span class="notbold">Einband: </span>Taschenbuch<br><span class="notbold">Reihe: </span>für Dummies<br><span class="notbold">ISBN: </span>9783527710034			</div>
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						<h1><a href="_9783527710034_inhalt.html">Inhaltsverzeichnis</a></h1>
						<p><table><tr><td></td><td>Über den Autor</td><td>9</td></tr><tr><td></td><td>Danksagung</td><td>9</td></tr><tr><td></td><td>Einleitung</td><td>17</td></tr><tr><td></td><td>Zu diesem Buch</td><td>17</td></tr><tr><td></td><td>Konventionen in diesem Buch</td><td>18</td></tr><tr><td></td><td>Törichte Annahmen über den Leser</td><td>18</td></tr><tr><td></td><td>Wie dieses Buch aufgebaut ist</td><td>18</td></tr><tr><td></td><td>Teil I: Grundlegende lineare Algebra</td><td>19</td></tr><tr><td></td><td>Teil II: Viel mehr lineare Algebra</td><td>19</td></tr><tr><td></td><td>Teil III: Eindimensionale Analysis</td><td>19</td></tr><tr><td></td><td>Teil IV: Der Top-Ten-Teil</td><td>20</td></tr><tr><td></td><td>Symbole in diesem Buch</td><td>20</td></tr><tr><td></td><td>Wie es weitergeht</td><td>21</td></tr><tr><td></td><td>Teil</td><td>1</td></tr><tr><td></td><td>Grundlegende lineare Algebra</td><td>23</td></tr><tr><td></td><td>Kapitel</td><td>1</td></tr><tr><td></td><td>Die Grundlagen der Mathematik: Logik, Mengen und Zahlen</td><td>25</td></tr><tr><td></td><td>Aussagenlogik - die Sprache der Mathematik verstehen</td><td>25</td></tr><tr><td></td><td>Wörter erfinden: die Definition</td><td>26</td></tr><tr><td></td><td>Wörter verbinden: die Aussage</td><td>27</td></tr><tr><td></td><td>Rasiermesserscharfe Logik - eine Basis für alle Mathematik</td><td>27</td></tr><tr><td></td><td>Logisch schreiben: Symbole, Symbole</td><td>29</td></tr><tr><td></td><td>Mengen und Relationen</td><td>29</td></tr><tr><td></td><td>Eine Menge Mengen</td><td>30</td></tr><tr><td></td><td>Verbundmengen</td><td>33</td></tr><tr><td></td><td>Zahlen, Zahlen, noch mehr Zahlen</td><td>33</td></tr><tr><td></td><td>Mit Hilfe der Logik zählen lernen</td><td>34</td></tr><tr><td></td><td>Die Sache mit den Schulden - Negative Zahlen</td><td>36</td></tr><tr><td></td><td>Die ganzen Zahlen zerbrechen - Rationale Zahlen</td><td>36</td></tr><tr><td></td><td>Da fehlt doch was - Reelle Zahlen</td><td>37</td></tr><tr><td></td><td>Komplex muss nicht kompliziert sein - komplexe Zahlen</td><td>40</td></tr><tr><td></td><td>Eine Wurzel aus -1: Die komplexen Zahlen entstehen</td><td>41</td></tr><tr><td></td><td>Rechnen mit komplexen Zahlen</td><td>43</td></tr><tr><td></td><td>Mathematik für Ingenieure I für Dummies</td><td></td></tr><tr><td></td><td>Polarkoordinaten</td><td>46</td></tr><tr><td></td><td>Komplexes Potenzieren und Wurzelziehen</td><td>48</td></tr><tr><td></td><td>Kapitel</td><td>2</td></tr><tr><td></td><td>Von Vektoren und Matrizen</td><td>51</td></tr><tr><td></td><td>Vektorräume</td><td>51</td></tr><tr><td></td><td>Mehr als Pfeile</td><td>52</td></tr><tr><td></td><td>Weitere Vektorräume entdecken</td><td>54</td></tr><tr><td></td><td>Vektorrechnung mit octave</td><td>57</td></tr><tr><td></td><td>Sind sie abhängig?</td><td>60</td></tr><tr><td></td><td>Eine Basis eröffnet die Dimensionen</td><td>63</td></tr><tr><td></td><td>Skalarprodukte und Normen: Längenmessung!</td><td>64</td></tr><tr><td></td><td>Lineare Abbildungen</td><td>70</td></tr><tr><td></td><td>Ganz einfach linear! Eine formale Definition der linearen Abbildung</td><td>70</td></tr><tr><td></td><td>Dies also ist der Abbildung Kern</td><td>72</td></tr><tr><td></td><td>Lineare Abbildungen und Spaltenvektoren</td><td>74</td></tr><tr><td></td><td>Mehrspaltiges: Matrizen</td><td>76</td></tr><tr><td></td><td>Zeilen zuerst, Spalten später</td><td>76</td></tr><tr><td></td><td>Matrizenräume sind Vektorräume</td><td>78</td></tr><tr><td></td><td>Matrixalgebra - mancherlei Matrizen multiplizieren</td><td>78</td></tr><tr><td></td><td>Matrizen sind - lineare Abbildungen!</td><td>85</td></tr><tr><td></td><td>Kapitel</td><td>3</td></tr><tr><td></td><td>Lineare Gleichungssysteme</td><td>89</td></tr><tr><td></td><td>Matrizen und lineare Gleichungssysteme</td><td>89</td></tr><tr><td></td><td>Für Schreibfaule - kurz und knapp mit Matrizen</td><td>90</td></tr><tr><td></td><td>Ja, geht das denn? Die Kerne kehren zurück</td><td>91</td></tr><tr><td></td><td>Matrizenadel: Von Zeilen- und Spaltenrang</td><td>93</td></tr><tr><td></td><td>Ja, das geht! Der Rang macht's möglich: Lösbarkeit</td><td>98</td></tr><tr><td></td><td>Determinanten bestimmen zur Lösung linearer Gleichungssysteme</td><td>100</td></tr><tr><td></td><td>Bäumchen wechsle dich oder Permutationen</td><td>100</td></tr><tr><td></td><td>Igitt! Determinanten</td><td>103</td></tr><tr><td></td><td>Nicht gar so eklig: Rekursiv geht's gut!</td><td>104</td></tr><tr><td></td><td>Rechnen mit Determinanten und nochmal: Lösbarkeit von</td><td></td></tr><tr><td></td><td>Gleichungssystemen</td><td>108</td></tr><tr><td></td><td>Inverse Matrix - Kehrwerte bei Matrizen</td><td>110</td></tr><tr><td></td><td>Gauß-Algorithmus: Im Halbschlaf Gleichungssysteme lösen</td><td>115</td></tr><tr><td></td><td>Gestaffelt ist's einfach - Rückwärtslösen</td><td>115</td></tr><tr><td></td><td>Endlich konkret: das Eliminationsverfahren</td><td>117</td></tr><tr><td></td><td>Abhängige Spalten, was nun?</td><td>121</td></tr><tr><td></td><td>Aufwand für Gauß und Cramer</td><td>124</td></tr><tr><td></td><td>Nicht nur einzelne Gleichungssysteme: Berechnung der Inversen</td><td>5</td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td>Teil</td><td>Ii</td></tr><tr><td></td><td>Viel mehr lineare Algebra 13 /</td><td></td></tr><tr><td></td><td>Kapitel h</td><td></td></tr><tr><td></td><td>Eigenwerte und EigenVektoren</td><td>133</td></tr><tr><td></td><td>Das Eigenwertproblem - kein Minderwertigkeitskomplex</td><td>133</td></tr><tr><td></td><td>Ganz charakteristisch, die Gleichung</td><td>135</td></tr><tr><td></td><td>Eigenwerte sind Nullstellen des charakteristischen Polynoms</td><td>136</td></tr><tr><td></td><td>Ganz allein meine! Berechnung der Eigenvektoren</td><td>138</td></tr><tr><td></td><td>Einige Eigenschaften von Eigenwerten</td><td>141</td></tr><tr><td></td><td>Ein Platz für die Eigenvektoren: der Eigenraum</td><td>143</td></tr><tr><td></td><td>Eigenwerte von Dreiecks- und Diagonalmatrizen</td><td>145</td></tr><tr><td></td><td>Ähnliche Matrizen</td><td>146</td></tr><tr><td></td><td>Diagonalähnliche Matrizen</td><td>147</td></tr><tr><td></td><td>Symmetrische und hermitesche Matrizen</td><td>149</td></tr><tr><td></td><td>Symmetrische Matrizen</td><td>150</td></tr><tr><td></td><td>Orthonormierte Eigenvektoren</td><td>153</td></tr><tr><td></td><td>Orthogonalmatrizen</td><td>154</td></tr><tr><td></td><td>Symmetrische und orthogonale Matrizen</td><td>156</td></tr><tr><td></td><td>Kapitel</td><td>5</td></tr><tr><td></td><td>Quadratische Formen und Ausgleichsrechnung</td><td>157</td></tr><tr><td></td><td>Ellipsengleichungen und quadratische Formen</td><td>157</td></tr><tr><td></td><td>Basiswechsel</td><td>160</td></tr><tr><td></td><td>Hauptachsentransformation</td><td>161</td></tr><tr><td></td><td>Der Physik auf der Spur: Lineare Ausgleichsrechnung</td><td>163</td></tr><tr><td></td><td>Orthogonalität</td><td>165</td></tr><tr><td></td><td>Orthogonalprojektion</td><td>166</td></tr><tr><td></td><td>Ausgleichsrechnung praktisch</td><td>167</td></tr><tr><td></td><td>Kapitel</td><td>6</td></tr><tr><td></td><td>Ein Wenig Dreidimensionales</td><td>173</td></tr><tr><td></td><td>Nicht nur für Piloten: Orientierung in 3D</td><td>173</td></tr><tr><td></td><td>Oben und unten - Ebenen unterteilen den Raum</td><td>173</td></tr><tr><td></td><td>Das Vektorprodukt</td><td>176</td></tr><tr><td></td><td>Mathematik für Ingenieure I für Dummies</td><td></td></tr><tr><td></td><td>Teil</td><td>III</td></tr><tr><td></td><td>Eindimensionale Anatysis</td><td>183</td></tr><tr><td></td><td>Kapitel</td><td>7</td></tr><tr><td></td><td>Folgen und Grenzwerte</td><td>185</td></tr><tr><td></td><td>Räume mit Abstand</td><td>185</td></tr><tr><td></td><td>Topologie: die Frage nach den nachbarschaftlichen Beziehungen</td><td>185</td></tr><tr><td></td><td>Rand- und innere Punkte</td><td>189</td></tr><tr><td></td><td>Häufungspunkte</td><td>192</td></tr><tr><td></td><td>Folgen</td><td>195</td></tr><tr><td></td><td>Grenzwerte von Folgen</td><td>198</td></tr><tr><td></td><td>Cauchy-Folgen</td><td>200</td></tr><tr><td></td><td>Auf dem Weg zur Analysis: Reelle Zahlenfolgen</td><td>203</td></tr><tr><td></td><td>Mit den Folgen rechnen</td><td>204</td></tr><tr><td></td><td>Kapitel</td><td>8</td></tr><tr><td></td><td>Stetigkeit</td><td>209</td></tr><tr><td></td><td>Grenzwerte reellwertiger Funktionen</td><td>209</td></tr><tr><td></td><td>Rechenregeln für Grenzwerte einer Funktion</td><td>212</td></tr><tr><td></td><td>Springen oder nicht springen: Stetigkeit</td><td>214</td></tr><tr><td></td><td>Ohne abzusetzen oder e-S: Stetigkeitsdefinitionen</td><td>215</td></tr><tr><td></td><td>Rechenregeln für stetige Funktionen</td><td>216</td></tr><tr><td></td><td>Eigenschaften stetiger Funktionen</td><td>217</td></tr><tr><td></td><td>Kapitel</td><td>9</td></tr><tr><td></td><td>Differentialrechnung</td><td>221</td></tr><tr><td></td><td>Die Ableitung</td><td>221</td></tr><tr><td></td><td>Vom Differenzenquotienten zum Differentialquotienten</td><td>221</td></tr><tr><td></td><td>Und geometrisch ist das auch!</td><td>224</td></tr><tr><td></td><td>Vorsicht: Nicht knicken! Differenzieren und Stetigkeit</td><td>225</td></tr><tr><td></td><td>Die Ableitung regeln</td><td>228</td></tr><tr><td></td><td>Ableitungsketten - verschachtelte Funktionen</td><td>231</td></tr><tr><td></td><td>Haufenweise Beispiele zur Kettenregel</td><td>232</td></tr><tr><td></td><td>Ableitung von Umkehrfunktionen</td><td>236</td></tr><tr><td></td><td>Wiederholtes Differenzieren: Höhere Ableitungen</td><td>238</td></tr><tr><td></td><td>Play it again, Sam! Ableitungen ableiten</td><td>238</td></tr><tr><td></td><td>Funktionen vom Feinsten - stetige Differenzierbarkeit</td><td>240</td></tr><tr><td></td><td>Ganz oben und ganz unten - Maxima und Minima</td><td>242</td></tr><tr><td></td><td>Globale und lokale Extremstellen</td><td>242</td></tr><tr><td></td><td>Bestimmung von Extremstellen</td><td>243</td></tr><tr><td></td><td>Der Mittelwertsatz - gerade mit krumm vergleichen</td><td>245</td></tr><tr><td></td><td>Ein Extremum muss sein: der Satz von Rolle</td><td>246</td></tr><tr><td></td><td>Schief geht es auch: der Mittelwertsatz</td><td>247</td></tr><tr><td></td><td>Grenzwerte ableiten und die Regeln von de l'Hospital</td><td>248</td></tr><tr><td></td><td>Kurvendiskussion</td><td>252</td></tr><tr><td></td><td>Kapitel</td><td>10</td></tr><tr><td></td><td>Bestimmte, unbestimmte und uneigentliche Integrale</td><td>261</td></tr><tr><td></td><td>Ein bestimmtes Integral</td><td>261</td></tr><tr><td></td><td>Krummlinige Flächen berechnen</td><td>262</td></tr><tr><td></td><td>Einfache Rechenregeln für bestimmte Integrale</td><td>267</td></tr><tr><td></td><td>Und jetzt umgekehrt: Stammfunktionen</td><td>270</td></tr><tr><td></td><td>Der Hauptsatz der Differential- und Integralrechnung</td><td>271</td></tr><tr><td></td><td>Das unbestimmte Integral</td><td>274</td></tr><tr><td></td><td>Alle meine Stammfunktionen</td><td>274</td></tr><tr><td></td><td>Nicht auf Sand gebaut: Grundintegrale</td><td>277</td></tr><tr><td></td><td>Was ist eigentlich ein uneigentliches Integral?</td><td>278</td></tr><tr><td></td><td>Die Sache mit den Randpunkten</td><td>278</td></tr><tr><td></td><td>Und wieder einmal: Grenzwerte</td><td>280</td></tr><tr><td></td><td>Vergleichskriterien</td><td>281</td></tr><tr><td></td><td>Parameterintegrale</td><td>285</td></tr><tr><td></td><td>Eigenschaften eigentlicher Parameterintegrale</td><td>285</td></tr><tr><td></td><td>Variable Integrationsgrenzen</td><td>287</td></tr><tr><td></td><td>Uneigentliche Parameterintegrale</td><td>289</td></tr><tr><td></td><td>Kapitel</td><td>11</td></tr><tr><td></td><td>Differenzieren ist Handu/erk - Integrieren eine Kunstf</td><td>291</td></tr><tr><td></td><td>Scheibchenweise integrieren: Partielle Integration</td><td>291</td></tr><tr><td></td><td>Hier hilft die Produktregel</td><td>291</td></tr><tr><td></td><td>Unbestimmt: Partielle Integration zur Bestimmung von Stammfunktionen</td><td>292</td></tr><tr><td></td><td>Und bestimmt! Partielle Integration bei bestimmten Integralen</td><td>295</td></tr><tr><td></td><td>Die Schwierigkeiten verstecken: Substitution</td><td>297</td></tr><tr><td></td><td>Hin- und hersubstituieren</td><td>298</td></tr><tr><td></td><td>Sinus- und Kosinusintegrale</td><td>299</td></tr><tr><td></td><td>Und noch eine Variante der Substitution</td><td>301</td></tr><tr><td></td><td>Partialbruchzerlegung - Integrale rationaler Funktionen</td><td>303</td></tr><tr><td></td><td>Zerlegung in einfache Brüche</td><td>304</td></tr><tr><td></td><td>Zwei Sorten Partialbrüche bleiben übrig</td><td>305</td></tr><tr><td></td><td>Partialbruchzerlegung bei unbestimmter Integration</td><td>310</td></tr><tr><td></td><td>Mathematik für Ingenieure I für Dummies</td><td></td></tr><tr><td></td><td>Kapitel</td><td>12</td></tr><tr><td></td><td>Reihen</td><td>313</td></tr><tr><td></td><td>Immer längere Summen: Unendliche Reihen</td><td>313</td></tr><tr><td></td><td>Bausteine stapeln oder Schildkrötenrennen</td><td>314</td></tr><tr><td></td><td>Alternierende Reihen: Schritt vor, Schritt zurück</td><td>321</td></tr><tr><td></td><td>Absolute Konvergenz? Unbedingt!</td><td>321</td></tr><tr><td></td><td>Wann konvergiert's? - Cauchy, Leibniz und Co</td><td>325</td></tr><tr><td></td><td>Potenzreihen</td><td>330</td></tr><tr><td></td><td>Potenzreihen oder unendlich lange Polynome</td><td>330</td></tr><tr><td></td><td>Wo konvergiert's denn?</td><td>331</td></tr><tr><td></td><td>Was ist das denn? Eine Funktion!</td><td>334</td></tr><tr><td></td><td>Differentiation und Integration von Potenzreihen - Stück für Stück</td><td>339</td></tr><tr><td></td><td>Taylorreihen</td><td>342</td></tr><tr><td></td><td>Funktionen ertasten: Approximation durch Polynome</td><td>343</td></tr><tr><td></td><td>Den Spieß umdrehen - Funktionen als Reihe</td><td>344</td></tr><tr><td></td><td>Des Schneiders Trickkiste: Taylorentwicklung für Dummies</td><td>350</td></tr><tr><td></td><td>Ted W</td><td></td></tr><tr><td></td><td>ber Top-Ten-Teil</td><td>353</td></tr><tr><td></td><td>Kapitel</td><td>13</td></tr><tr><td></td><td>Zehn Dos and Don'ts der linearen Algehra</td><td>355</td></tr><tr><td></td><td>Kapitel U</td><td></td></tr><tr><td></td><td>Zehn nichtige Punkte in der Anatgsis</td><td>359</td></tr><tr><td></td><td>Kapitel</td><td>15</td></tr><tr><td></td><td>Wie man einen Mathekurs erfolgreich überlebt</td><td>363</td></tr><tr><td></td><td>Mathematik und Psychologie</td><td>363</td></tr><tr><td></td><td>Nicht locker lassen!</td><td>364</td></tr><tr><td></td><td>Glauben Sie nichts!</td><td>365</td></tr><tr><td></td><td>Üben Sie! Üben Sie!</td><td>366</td></tr><tr><td></td><td>AnhangA</td><td></td></tr><tr><td></td><td>Lösungen der Aufgaben 36</td><td>7</td></tr><tr><td></td><td><div></td><td>383</td></tr><tr><td></td><td></div>
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