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Researches in the Calculus of Variations, Principally on the Theory of Discontinuous Solutions: An Essay to Which the Adams Prize Was Awarded in the University of Cambridge in 1871
Excerpt from Researches in the Calculus of Variations, Principally on the Theory of Discontinuous Solutions: An Essay to Which the Adams Prize Was Awarded in the University of Cambridge in 1871
The subject of this Essay was prescribed in the following terms by the Examiners:
The Adams Prize.
A determination of the circumstances under which discontinuity of any kind presents itself in the solution of a problem of maximum or minimum in the Calculus of Variations, and applications to particular instances.
It is expected that the discussion of the instances should be exemplified as far as possible geometrically, and that attention be especially directed to cases of real or supposed failure of the Calculus.
It was after much hesitation that I resolved to discuss the subject; the fact that it had given rise to some controversy, however, naturally led me to enforce what I believed to be the correct and adequate explanation of the difficulties which had been raised.
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.
The subject of this Essay was prescribed in the following terms by the Examiners:
The Adams Prize.
A determination of the circumstances under which discontinuity of any kind presents itself in the solution of a problem of maximum or minimum in the Calculus of Variations, and applications to particular instances.
It is expected that the discussion of the instances should be exemplified as far as possible geometrically, and that attention be especially directed to cases of real or supposed failure of the Calculus.
It was after much hesitation that I resolved to discuss the subject; the fact that it had given rise to some controversy, however, naturally led me to enforce what I believed to be the correct and adequate explanation of the difficulties which had been raised.
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.
292 pages, Paperback
First published April 4, 2010
About the author
Isaac Todhunter
201 books3 followersEnglish mathematician known for his writings on the history of mathematics.
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