Vektoranalysis und Differentialformen: Fundamentale Werkzeuge der Mathematik (essentials)
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Dieter Riebesehl schlägt in diesem essential die Brücke von der klassischen Vektoranalysis zum Formalismus der Differentialformen.
Die Vektoranalysis behandelt Vektorfelder, meist im zwei- oder dreidimensionalen Raum, und ist ein grundlegendes Werkzeug für Physiker, Ingenieure und Techniker. Die zentralen Definitionen werden sorgfältig motiviert und dann die wichtigsten Aussagen bis hin zu den Integralsätzen von Gauß und Stokes hergeleitet. Die Darstellung ist möglichst elementar und vermeidet darüberhinausgehende Konzepte wie Mannigfaltigkeiten.
Die Vektoranalysis hat einen gewissen Mangel an Eleganz, der sich darin äußert, dass sie sich nicht leicht auf mehr als drei Dimensionen verallgemeinern lässt und unnötig viele ähnliche Konzepte verwendet. Die Sprache der Differentialformen kommt mit weniger Konzepten aus, ermöglicht besonders knappe Formulierungen der Integralsätze und ist leicht auf beliebige Dimensionen verallgemeinerbar.
In diesem essential wird die Übersetzung der Vektoranalysis in die Sprache der Differentialformen anschaulich und die Eleganz der neuen Formulierung deutlich gemacht.
Details
- Publisher
- Springer Berlin Heidelberg
- Author
- Dieter Riebesehl
- Format
- Paperback
- Published
- Aug 30, 2024
- ISBN-13
- 9783662696637
- Pages
- 56
- Printing
- Printed on demand
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