Elements of the Theory of Functions of a Complex Variable: With Especial Reference to the Methods of Riemann (Classic Reprint) - Softcover

Durège, H.

Softcover

ISBN 10: 1330368487 ISBN 13: 9781330368480

Verlag: Forgotten Books, 2018

Inhaltsangabe

Excerpt from Elements of the Theory of Functions of a Complex Variable: With Especial Reference to the Methods of Riemann

To follow the gradual development of the theory of imagi nary quantities is especially interesting, for the reason that we can clearly perceive with what difficulties is attended the introduction of ideas, either not at all known before, or at least not sufficiently current. The times at which negative, fractional and irrational quantities were introduced into mathematics are so far removed from us, that we can form no adequate conception of the difficulties which the intro duction of those quantities may have encountered. Moreover, the knowledge of the nature of imaginary quantities has helped us to a better understanding of negative, fractional and irrational quantities, a common bond closely uniting them all.

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Excerpt from Elements of the Theory of Functions of a Complex Variable: With Especial Reference to the Methods of Riemann

Numerous additions have been made to Section IX., which treats of multiply connected surfaces. If Riemann's fundamental proposition on these surfaces be enunciated in such a form that merely simply connected pieces are formed by both modes of resolution, - as is ordinarily, and was also in § 49, the case, - then it must be supplemented for further applications. Such supplementary matter was given in § 52 in the classification of surfaces, and in § 53, V. But if we express the fundamental proposition in the form in which Riemann originally established it, in which merely simply connected pieces are formed by only one mode of resolution, while the pieces resulting from the other mode of resolution may or may not be simply connected, then all difficulties are obviated, and the conclusions follow immediately without requiring further expedients.

This was shown in a supplementary note at the end of the book.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 1330368487
• ISBN 13: 9781330368480
• Einband: Tapa blanda
• Anzahl der Seiten: 310
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