"Dieses Lehrbuch gibt eine Einführung in das Lösen von Differentialgleichungen (Dgl). Behandelt werden sowohl gewöhnliche als auch partielle Dgl. Die mathematische Theorie wird für exakte und numerische Lösungsmethoden soweit dargestellt, wie es für Anwender erforderlich ist. Auf Beweise wird verzichtet, dafür werden notwendige Formeln, Sätze und Methoden anhand von Beispielen erläutert. Außerdem wird die Problematik von Differenzengleichungen und Integralgleichungen skizziert. Ein zweiter Schwerpunkt des Buches liegt auf der Anwendung der Computeralgebra- und Mathematiksysteme MATHCAD und MATLAB zur Lösung von Dgl. Darüber hinaus eignet sich das Buch als Nachschlagewerk: Der Leser kann für praktisch auftretende Dgl Eigenschaften und Lösungsmethoden finden und diese für die Lösung mittels MATHCAD und MATLAB heranziehen. Das Buch ist geschrieben für Ingenieure, Natur- und Wirtschaftswissenschaftler. TOC: Einleitung.- Differenzengleichungen.- Differentialgleichungen.- Gewöhnliche Differentialgleichungen.- Gewöhnliche Differentialgleichungen erster Ordnung.- Gewöhnliche Differentialgleichungen zweiter Ordnung.- Gewöhnliche Differentialgleichungen n-ter Ordnung.- Systeme gewöhnlicher Differentialgleichungen erster Ordnung.- Integralgleichungen.- Partielle Differentialgleichungen.- Partielle Differentialgleichungen erster Ordnung.- Partielle Differentialgleichungen zweiter Ordnung.- Numerische Lösung partieller Differentialgleichungen.- Zusammenfassung.- Anhang A: Mathcad, Matlab, Femlab.- Anhang B: Funktionen mit Mathcad und Matlab.- Anhang C: Grafische Darstellungen mit Mathcad und Matlab.- Anhang D: Lösungen von Gleichungen mit Mathcad und Matlab.- Anhang E: Programmierung mit Mathcad und Matlab.- Literatur- und Sachverzeichnis."
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Appl. Mathematics/Computational Methods of Engineering.
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