Einführung in Die Vektorrechnung: Für Naturwissenschaftler, Chemiker Und Ingenieure

Name: Einführung in Die Vektorrechnung: Für Naturwissenschaftler, Chemiker Und Ingenieure
Brand: Springer
SKU: 9783642533426
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ISBN13: 9783642533426
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: January 1, 1969
Pages: 214
Original Price: EUR 51.39
Language: German
Edition: 2. Aufl. 1969
Item Weight: 368 grams
BISAC Subject(s): General

About The Book

1. Die Vektordefinition und einfachere Gesetzmäßigkeiten.- 1.1 Skalare und Vektoren.- 1.2 Die Summe und die Differenz von Vektoren.- 1.3 Die Multiplikation eines Vektors mit einem Skalar.- 1.4 Einsvektoren.- 1.5 Die lineare Abhängigkeit von Vektoren.- 1.6 Die Zerlegung eines Vektors in Komponenten.- 1.7 Das kartesische Koordinatensystem.- 1.8 Übungsaufgaben Nr. 1 bis Nr. 14.- 2. Produkte zweier Vektoren.- 2.1 Das skalare Produkt.- 2.2 Geometrische und physikalische Anwendungsbeispiele zum skalaren Produkt.- 2.3 Die Komponentendarstellung des skalaren Produktes.- 2.4 Die Transformation kartesischer Komponenten.- 2.5 Übungsaufgaben zum skalaren Produkt Nr. 15 bis Nr. 34.- 2.7 Die Komponentendarstellung des dyadischen Produktes.- 2.8 Das Vektorprodukt.- 2.9 Geometrische und physikalische Anwendungsbeispiele zum Vektorprodukt.- Das Drehmoment eines Kräftepaares.- 2.10 Die Komponentendarstellung des Vektorproduktes.- 2.11 Übungsaufgaben zum Vektorprodukt und zum dyadischen Produkt Nr. 35 bis Nr. 43.- 3. Die Differentiation von Vektoren nach Skalaren.- 3.1 Die Definition des Differentialquotienten eines Vektors nach einem Skalar.- 3.2 Die Differentiation von Produkten von Vektoren.- 3.3 Anwendungsbeispiele aus der Geometrie.- 3.4 Anwendungsbeispiele aus der Physik.- 3.5 Übungsaufgaben Nr. 44 bis Nr. 55.- 4. Mehrfache Produkte von Vektoren.- 4.1 Das Spatprodukt.- 4.2 Der Entwicklungssatz.- 4.3 Das gemischte Dreifachprodukt.- 4.4 Die Überschiebung zweier dyadischer Produkte.- 4.5 Anwendungsbeispiele aus der Geometrie.- 4.6 Anwendungsbeispiele aus der Physik.- 4.7 Übungsaufgaben Nr. 56 bis Nr. 66.- 5. Der Gradient.- 5.1 Das Skalarfeld und der Gradient.- 5.2 Das Gradientenfeld.- 5.3 Anwendungsbeispiele.- 5.4 Das Vektorfeld und der Vektorgradient.- 5.5Übungsaufgaben Nr. 67 bis Nr. 91.- 6. Die Divergenz und die Rotation.- 6.1 Das Quellenfeld und der Begriff der Divergenz.- 6.2 Der Gaußsche Integralsatz.- 6.3 Anwendungsbeispiele.- 6.4 Das Wirbelfeld und der Begriff der Rotation.- 6.5 Der Stokessche Integralsatz.- 6.6 Anwendungsbeispiele.- 6.7 Übungsaufgaben Nr. 92 bis Nr. 117.- 7. Erweiterte räumliche Differentiation.- 7.1 Der Nabla-Operator.- 7.2 Die räumliche Differentiation von Produkten.- 7.3 Die Kettenregel bei räumlicher Differentiation.- 7.4 Mehrfache räumliche Differentiation.- 7.5 Anwendungsbeispiele.- 7.6 Übungsaufgaben Nr. 118 bis Nr. 130.- 8. Zylinder- und Kugelkoordinaten.- 8.1 Zylinderkoordinaten.- 8.2 Differentiationen in Zylinderkoordinaten.- 8.3 Kugelkoordinaten.- 8.4 Differentiationen in Kugelkoordinaten.- 8.5 Flächen- und Volumenintegrale in Zylinderkoordinaten.- 8.6 Anwendungsbeispiele.- 8.7 Übungsaufgaben Nr. 131 bis Nr. 148.

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