Geometrische Strukturen Der Kontinuumsphysik: Raum-Zeit-Exkursionen Von Der Euklidischen Zur Riemannschen Geometrie
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Dieses Buch liefert anschauliche und teilweise detaillierte Einblicke in die Strukturen der Euklidischen und Riemannschen Geometrie sowie deren Verschmelzung mit den Gegenständen der Physik. Entwickelt wird eine Analysis auf differenzierbaren Mannigfaltigkeiten. Im Mittelpunkt stehen dabei die sorgfältige Herausarbeitung von Ableitungsbegriffen (kovariante Ableitung, Lie-Ableitung, äu ere Ableitung) und des Integralbegriffes auf der Basis von Differentialformen.
Anhand der Raumzeit-Problematik und mit Exkursionen in die Elektrodynamik, die relativistische Gravitation und die Kontinuumsmechanik werden Verbindungen zwischen Geometrie und Physik hergestellt sowie physikalische Konzepte aus geometrischer Sicht interpretiert.
Im gesamten Buch flankieren möglichst einfache Beschreibungen und Erläuterungen die präzisen Ausdrücke der Formelsprache. Darüber hinaus tragen zahlreiche Beispiele und Skizzen zum Verständnis bei. Auch Hinweise, die dem versierten Leser überflüssigerscheinen mögen, werden zugunsten der im Lernprozess stehenden Leser nicht ausgelassen. Klassische - teils sehr technische - Beweise werden mitunter nur angedeutet oder durch Plausibilitätserklärungen ersetzt.
Vorausgesetzt werden Grundlagen der Differential- und Integralrechnung sowie der linearen Algebra - insbesondere der Umgang mit Matrizen, Determinanten und die Lösung gewöhnlicher Differentialgleichungen. Im ersten Kapitel findet sich ein behutsam hinführender Überblick zu den nötigen algebraischen Grundlagen.
Prof. Dr. Heinz Gründemann lehrte 1993-2008 Mathematik für angehende Mathematiker, Physiker und Maschinenbauingenieure an der Hochschule Mittweida.
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