Theory of Differential Equations, Vol. 3 (Classic Reprint): Part II. Ordinary Equations, Not Linear: Part II. Ordinary Equations, Not Linear (Classic Reprint) - Softcover

Forsyth, Andrew Russell

9781334018237: Theory of Differential Equations, Vol. 3 (Classic Reprint): Part II. Ordinary Equations, Not Linear: Part II. Ordinary Equations, Not Linear (Classic Reprint)

Softcover

ISBN 10: 1334018235 ISBN 13: 9781334018237

Verlag: Forgotten Books, 2018

Alle Exemplare dieser ISBN-Ausgabe

0 Gebraucht

1 Neu

Von EUR 22,78

This book delves into the theoretical framework surrounding differential equations, particularly those equations that are nonlinear and of the first order. The author employs a systematic approach, exploring concepts from their origin, elucidating their historical evolution, and examining the analytical tools utilized in their study. The book's primary focus is the investigation of the behavior of integrals associated with differential equations in the vicinity of singular points and singularities. The author introduces essential background material, including the existence and uniqueness of integrals and the reduction of systems to canonical forms. The exploration then extends to more complex scenarios involving accidental singularities and essential singularities, providing a comprehensive analysis of the integral behavior in each case. The book concludes with a detailed examination of the reduced forms of systems of equations involving two dependent variables, offering a thorough understanding of the construction and characteristics of these forms.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Rese�a del editor

Excerpt from Theory of Differential Equations, Vol. 3: Part II. Ordinary Equations, Not Linear

Complete integral of a special system of two equations in a canonical reduced form: with inferences sug gested as to the complete integral of a general system of two equations.

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.

Rese�a del editor

Excerpt from Theory of Differential Equations, Vol. 3: Part II. Ordinary Equations, Not Linear
The importance of this equation does not lie mainly in the comparative simplicity of the forms of differential equations which are suggested as possible equivalents of the original system, but is rather constituted by an invariantive property which it possesses, viz. Whatever be the intermediate linear transformations effected upon the variables x, the roots 7t of the determinantal equation are entirely independent of those intermediate transformations. The formal proof of this property is practically identical with the formal proof of the invariantive character of the fundamental equation appertaining to a singularity of an ordinary linear equation of order n; it is as follows.
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.

��ber diesen Titel� kann sich auf eine andere Ausgabe dieses Titels beziehen.