Download Angewandte Mathematik mit Mathcad. Lehr- und Arbeitsbuch 2: by Josef Trölß PDF

By Josef Trölß

Computer-Algebra-Systeme (CAS) und computerorientierte numerische Verfahren (CNV) vereinfachen die Anwendung der Mathematik. Mathcad verbindet mathematische Formeln, Berechnungen, Texte, Grafiken usw. in einem Arbeitsblatt. Der Band stellt die computerorientierte Anwendung der Mathematik in Beispielen dar und simuliert Berechnungen in anschaulicher Darstellung. Er richtet sich an Sch?ler, Studierende, Naturwissenschaftler sowie Anwender – speziell im technischen Bereich. Die three. Auflage wurde entsprechend der Mathcad model 14 ?berarbeitet.

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Read or Download Angewandte Mathematik mit Mathcad. Lehr- und Arbeitsbuch 2: Komplexe Zahlen und Funktionen, Vektoralgebra und Analytische Geometrie, Matrizenrechnung, Vektoranalysis, 3. Auflage PDF

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his
day-to-day
reference.

Extra resources for Angewandte Mathematik mit Mathcad. Lehr- und Arbeitsbuch 2: Komplexe Zahlen und Funktionen, Vektoralgebra und Analytische Geometrie, Matrizenrechnung, Vektoranalysis, 3. Auflage

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Komplexen Effektivwerten gerechnet und als Zeiger (ähnlich wie Vektoren) grafisch dargestellt werden. Die in der komplexen Form dargestellte sinusförmige Wechselspannung j˜ ω˜t φu u = ۘ e = Û ˜ ej˜φu ˜ ej˜ω˜t = Û ˜ ej˜ω˜t = j ˜ω˜t 2˜ U˜ e (2-16) erzeugt den gleichfrequenten sinusförmigen Wechselstrom j ˜ ω˜t φi i = Θe = Î ˜ ej˜φi ˜ ej˜ω˜t = Î ˜ ej˜ω˜t = j ˜ω˜t 2˜ I˜ e (2-17) Die komplexen Scheitelwerte Û und Î hängen im komplexen Bereich und deren Beträge im reellen Bereich über den Faktor 2 mit den Effektivwerten zusammen: Û= 2 ˜ Ueff = 2˜ U ; Î = 2 ˜ Ieff = 2˜ I; (2-18) Û= 2 ˜ Ueff = 2˜ U ; 2 ˜ Ieff = 2˜ I.

Bergang von der reellen Form zur komplexen Form: j ˜ ω˜t φ1 y1 = Â1 ˜ e = j˜φ1 1˜ e j˜ φ1 Â1  Â1 ˜ e j ˜ ω˜t φ2 y2 = Â2 ˜ e j˜ φ2 Â2  Â2 ˜ e j˜ω˜t ˜e komplexe Schwingungsamplitude der 1. Schwingung = j˜φ2 2˜ e ·¸ ¸¹ § Â1 ˜ sin φ1  Â2 ˜ sin φ2 φs  atan ¨ ¨© Â1 ˜ cos φ1  Â2 ˜ cos φ2 Â1  Â2  2 ˜ Â1 ˜ Â2 ˜ cos φ1  φ2 j˜ω˜t ˜e komplexe Schwingungsamplitude der 2. Schwingung Seite 44 Komplexe Zahlen und Funktionen 2. 464j ) ˜ cm x- und y-Werte der Endpunkte der Zeigerteilstrecken des Zeigers 2 ˜ cm ¢2² § Âs · ¸ yys  zeiger ¨ © cm ¹ ˜ cm x- und y-Werte der Endpunkte der Zeigerteilstrecken des Summenzeigers ˜ cm Zeiger in der Gauß'schen Ebene 10 9 8 7 yy1 6 cm 5 yy2 cm Âs  Â1  Â2 Â2 4 3 yys 2 cm 1 2 1 Â1 0 1 2 3 4 5 6 7 8 9 10 1 2 x y1 x y2 x ys   cm cm cm Abb.

Strom und Spannung sind in Phase, d. h. Mu = Mi und damit M = 0. Seite 52 Komplexe Zahlen und Funktionen Zeigerdiagramme (Scheitelwerte und Effektivwerte): Abb. 10 Z-Ebene: Widerstandsebene Y-Ebene: Leitwertebene Abb. 11 b) Widerstands- und Leitwertoperatoren der verlustfreien Spule L Abb. 12 Für eine Spule gilt das Induktionsgesetz u = us = L ˜ d i ( t) , (2-37) dt und in komplexer Darstellung (Permanenzprinzip - die Differentiation verläuft nach den gleichen Regeln wie im Reellen) u = L˜ d dt i.

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