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The Integration of Functions of a Single Variable, Vol. 2
Excerpt from The Integration of Functions of a Single Variable, Vol. 2
The reader who is familiar with the theory of algebraical functions and algebraical plane curves will no doubt find the treatment in Section V. Of the integrals of algebraical functions sketchy and inadequate. I hope, however, that he will bear in mind the great difficulty of presenting even an outline of the elements of so vast a subject in a short space and without presupposing a wider range of mathematical knowledge than I am at liberty to assume.
I have naturally not said much about particular devices which are only useful in special cases, but I have tried to show, where it is possible, how such devices find their place in the general theory. And I would strongly recommend any reader who is not already familiar with the general processes here explained to work through a number of examples (those for instance which have been set in the Mathe matical Tripos in recent years) using in each case both the general method and any special method which he may find better adapted to the particular case.
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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 reader who is familiar with the theory of algebraical functions and algebraical plane curves will no doubt find the treatment in Section V. Of the integrals of algebraical functions sketchy and inadequate. I hope, however, that he will bear in mind the great difficulty of presenting even an outline of the elements of so vast a subject in a short space and without presupposing a wider range of mathematical knowledge than I am at liberty to assume.
I have naturally not said much about particular devices which are only useful in special cases, but I have tried to show, where it is possible, how such devices find their place in the general theory. And I would strongly recommend any reader who is not already familiar with the general processes here explained to work through a number of examples (those for instance which have been set in the Mathe matical Tripos in recent years) using in each case both the general method and any special method which he may find better adapted to the particular case.
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.
69 pages, Hardcover
First published September 27, 2015
3 people want to read
About the author
G.H. Hardy
68 books148 followersGodfrey Harold Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis.
Non-mathematicians usually know him for A Mathematician's Apology, his essay from 1940 on the aesthetics of mathematics. The apology is often considered one of the best insights into the mind of a working mathematician written for the layman.
His relationship as mentor, from 1914 onwards, of the Indian mathematician Srinivasa Ramanujan has become celebrated. Hardy almost immediately recognized Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration "the one romantic incident in my life."
Non-mathematicians usually know him for A Mathematician's Apology, his essay from 1940 on the aesthetics of mathematics. The apology is often considered one of the best insights into the mind of a working mathematician written for the layman.
His relationship as mentor, from 1914 onwards, of the Indian mathematician Srinivasa Ramanujan has become celebrated. Hardy almost immediately recognized Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration "the one romantic incident in my life."
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