Theorie Der Partiellen Differentialgleichungen Erster Ordnung
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Das von der königl. belgischen Akademie der Wissenschaften preis- gekrönte, im Buchhandel längst vergriffene Werk von Mansion: "Theorie des equations aux derivees partielles du premier ordre" erscheint hiermit in neuer und zwar deutscher Ausgabe. Da das vortreffiiche Buch auch in Deutschland ungetheilte Anerkennung gefunden und hinlänglich bekannt ist, so dülfte es überflüssig sein, die Vorzüge desselben nochmals be- sonders hervorzuheben. Es mag nur darauf hingewiesen werden, dass das Mansion'sche Buch bisher das einzige geblieben ist, welches in so ein- gehender Weise die verschiedenen Methoden, welche zur Integration der partiellen Differentialgleichungen erster Ordnung vorgeschlagen wurden, historisch-kritisch beleuchtet, ihre Beziehungen zu einander klal'legt, ihre Vorzüge und Mängel gegenseitig abwägt und jedem der Begründer dieser Methoden .das Verdienst lässt, welches ihm zukommt. Es ist das einzige Werk dieser Art geblieben, einfach a.us dem Grunde, weil es seine Aufgabe gleich in vollkommener und unübertrefflicher Weise löste. Allerdings hat die Theorie der partiellen Differentialgleichungen erster Ordnung seit dem ersten Erscheinen des Mansion'schen Buches viele wichtige Erweiterungen und Verbesserungen elfahren und es sind auch seitdem, besonders in allerneuester Zeit, einige hochbedeutsame Werke über jene Theorie hervorgetreten; zum Theil aber sind dieselben mehr als Lehrbücher im engeren Sinne zu betrachten, denen es weniger auf die Hervorkehrung des historisch-kritischen Standpunktes als auf eine syste- matische Verarbeitung und Zusammenfassung des vorhandenen Materials ankommt, zum Theil sind dieselben, wie das hervorragend wichtige Werk von S ophus Lie: "Zur Theorie der Transformationsgruppen", dazu be- stimmt, der gesammten Theorie eine einheitliche Grundlage zu geben, sie
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