Absolute Analysis
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Das vorliegende Werk ist als Ergebnis von Vorlesungen entstanden, welche die Verfasser seit 1953 im Laufe von mehreren Jahren an den Universitäten Helsinki und Zürich gehalten haben. Die nachfolgende Einleitung gibt über die Tendenzen Aufschlu , die für unsere Darstellung der Grundlagen einer absoluten, koordinaten- und dimensionsfreien Infinitesimalrechnung ma gebend gewesen sind. Die Lektüre setzt an Vorkenntnissen nur wenig voraus; sie kann jedem Studierenden emp- fohlen werden, der mit dem üblichen, auf die Benutzung von Koordi- naten fu enden Aufbau der Elemente der analytischen Geometrie, der Differential- und Integralrechnung und der Theorie der Differential- gleichungen vertraut ist. Unsere Arbeit ist durch die Hilfe wesentlich erleichtert worden, die uns von mehreren Seiten zuteil geworden ist. Herr Ilppo Simo Louhi- vaara hat von Anfang bis zu Ende an der Herstellung dieses Werkes mit unermüdlichem Interesse und minutiöser Sorgfalt teilgenommen und durch zahlreiche sachliche und formelle Bemerkungen und Vor- schläge unsere Arbeit wesentlich gefördert. Für seine wertvolle, auf- opfernde Unterstützung sprechen wir hier unseren herzlichen Dank aus. Den Herren H. Keller, T. Klemola, T. Nieminen, Ph. Tondeur und K. 1. Virtanen, die unsere Darstellung im Manuskript gelesen haben, verdanken wir verschiedene wichtige kritische Bemerkungen. Unser Dank gilt auch Herrn Professor Dr. F. K. Schmidt für die Aufnahme dieses Werkes in die Reihe der Grundlehren der mathema- tischen Wissenschaften, und dem Springer-Verlag, der unseren Wünschen mit freundlicher Bereitwilligkeit entgegengekommen ist.
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