New PDF release: Angewandte Mathematik mit Mathcad, Lehr- und Arbeitsbuch:

By Josef Trölß

ISBN-10: 321129693X

ISBN-13: 9783211296936

ISBN-10: 3211296948

ISBN-13: 9783211296943

Computer-Algebra-Systeme (CAS) und computerorientierte numerische Verfahren (CNV) vereinfachen den praktischen Umgang mit der Mathematik ganz entscheidend und werden in immer weiteren Bereichen angewendet. Mathcad stellt dazu eine Vielfalt an Werkzeugen zur Verf?gung und verbindet mathematische Formeln, Berechnungen, Texte, Grafiken usw. in einem einzigen Arbeitsblatt. So lassen sich Berechnungen und ihre Resultate besonders einfach illustrieren, visualisieren und kommentieren. Dieses Lehr- und Arbeitsbuch, aus dem vierb?ndigen Werk "Angewandte Mathematik mit Mathcad", richtet sich vor allem an Sch?lerinnen und Sch?ler h?herer Schulen, Studentinnen und Studenten, Naturwissenschaftlerinnen und Naturwissenschaftler sowie Anwenderinnen und Anwender – speziell im technischen Bereich –, die sich ?ber eine computerorientierte Umsetzung mathematischer Probleme im Bereich der Potenzreihen, Taylorreihen, Laurentreihen, Fourierreihen, Fourier-Transformation, Laplace-Transformation, z-Transformation, Differentialgleichungen, Differenzengleichungen informieren wollen und dabei die Vorz?ge von Mathcad m?glichst effektiv n?tzen m?chten.

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Additional resources for Angewandte Mathematik mit Mathcad, Lehr- und Arbeitsbuch: Band 4: Reihen, Transformationen, Differential- und Differenzengleichungen German

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Die Amplitude (Scheitelwert) An und die Phasenlage M n des n-ten Gliedes ermittelt man bn § bn · 2 2 an  bn , tan M n =  aus an und bn durch: An = bzw. M n = arctan ¨ . an © an ¹ A3 ˜ sin 3 ˜ Z0 ˜ t  \ 3 A1 ˜ sin Z0 ˜ t  \ 1 A2 ˜ sin 2 ˜ Z0 ˜ t  \ 2 1. Harmonische oder Grundschwingung, 2. Harmonische oder 1. Oberschwingung, 3. Harmonische oder 2. Oberschwingung usw. Trägt man die Fourierkoeffizienten in Abhängigkeit der zugehörigen Frequenz in einem Diagramm auf, so erhält man das Amplituden- oder Frequenzspektrum (auch Linienspektrum genannt).

Glied abbricht ? e) Stellen Sie die Funktion und die Näherungspolynome bis zum 7. Grad grafisch dar. f) Stellen Sie den relativen Fehler im Vergleich von Funktion und Taylorpolynome grafisch dar. x f ( x)  e gegebene Funktion und Entwicklungsstelle x0  0 f ' ( 0) f ( x) = f ( 0)  1 ˜x f '' ( 0) 2 f ''' ( 0) 2 ˜x  3 3 Entwicklung der Funktion an der Stelle x 0 = 0 ˜ x  .... 10 -4 (e ist auf 3 Stellen genau). 01  10 Bereichsvariable 10 x0 8 6 f( x) p ( x) 4 f x0 2 4 2 0 2 2 4 n x  x  x0 Abb.

F ( x)  sin ( x) f ( x) = f ( 0)  gegebene Funktion und Entwicklungsstelle x0  0 f ' ( 0) 1 ˜x f '' ( 0) 2 2 ˜x  f ''' ( 0) 3 3 ˜ x  .... Seite 25 Entwicklung der Funktion an der Stelle x 0 = 0 Taylorreihen fx ( x  n)  konstantes Glid a 0 f ( 0) = sin ( 0) = 0 n d n a0 = 0 Ableitungen f ( x) dx 1. Ableitung an der Stelle 0 1 a1 = 1 0 2. Ableitung an der Stelle 0 a2 = 0 1 3. Ableitung an der Stelle 0 1 a3 =  3 fx ( x  1) o cos ( x) fx ( 0  1) o cos ( 0) 1 fx ( x  2) o sin ( x) fx ( 0  2) o sin ( 0) fx ( x  3) o cos ( x) fx ( 0  3) o cos ( 0) fx ( x  4) o sin ( x) fx ( 0  4) o sin ( 0) 0 4.

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Angewandte Mathematik mit Mathcad, Lehr- und Arbeitsbuch: Band 4: Reihen, Transformationen, Differential- und Differenzengleichungen German by Josef Trölß

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