A Treatise On The Differential Geometry Of Curves And Surfaces Classic Reprint

Author : Luther Pfahler Eisenhart
Publisher : Forgotten Books
Page : 490 pages
File Size : 45,7 Mb
Release : 2017-09-18
Category : Mathematics
ISBN : 1528484622

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A Treatise on the Differential Geometry of Curves and Surfaces (Classic Reprint) by Luther Pfahler Eisenhart Pdf

Excerpt from A Treatise on the Differential Geometry of Curves and Surfaces The remainder of the book may be divided into three parts. The first, consisting of Chapters II - VI, deals with the geometry of a sur face ih the neighborhood of a point and the developments therefrom, such as curves and systems of curves defined by differential equa tions. To a large extent the method is that of Gauss, by which the properties of a surface are derived from the discussion of two quad ratio differential forms. However, little or no space is given to the algebraic treatment of differential forms and their invariants. In addition, the method of moving axes, as defined in the first chapter, has been extended so as to be applicable to an investigation of the properties of surfaces and groups of surfaces. The extent of the theory concerning ordinary points is so great that no attempt has been made to consider the exceptional problems. For a discussion of such questions as the existence of integrals of differential equa tions and boundary conditions the reader must consult the treatises which deal particularly with these subjects. 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.

Author : Eisenhart Luther Pfahler
Publisher : Unknown
Page : 128 pages
File Size : 55,6 Mb
Release : 1901
Category : Electronic
ISBN : 0243847750

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Treatise On the Differential Geometry of Curves and Surfaces by Eisenhart Luther Pfahler Pdf

Author : Luther Pfahler Eisenhart
Publisher : Courier Corporation
Page : 496 pages
File Size : 41,6 Mb
Release : 2013-04-25
Category : Mathematics
ISBN : 9780486159461

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A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart Pdf

Created especially for graduate students by a leading writer on mathematics, this introduction to the geometry of curves and surfaces concentrates on problems that students will find most helpful.

Author : Luther Pfahler Eisenhart
Publisher : Forgotten Books
Page : 490 pages
File Size : 40,9 Mb
Release : 2015-06-15
Category : Mathematics
ISBN : 1451004672

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A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart Pdf

Excerpt from A Treatise on the Differential Geometry of Curves and Surfaces This book is a development from courses which I have given in Princeton for a number of years. During this time I have come to feel that more would be accomplished by my students if they had an introductory treatise written in English and otherwise adapted to the use of men beginning their graduate work. Chapter I is devoted to the theory of twisted curves, the method in general being that which is usually followed in discussions of this subject. But in addition I have introduced the idea of moving axes, and have derived the formulas pertaining thereto from the previously obtained Frenet-Serret formulas. In this way the student is made familiar with a method which is similar to that used by Darboux in the first volume of his Leçons, and to that of Cesaro in his Geometria Intrinseca. This method is not only of great advantage in the treatment of certain topics and in the solution of problems, but it is valuable in developing geometrical thinking. The remainder of the book may be divided into three parts. The first, consisting of Chapters II-VI, deals with the geometry of a surface in the neighborhood of a point and the developments therefrom, such as curves and systems of curves defined by differential equations. To a large extent the method is that of Gauss, by which the properties of a surface are derived from the discussion of two quadratic differential forms. However, little or no space is given to the algebraic treatment of differential forms and their invariants. In addition, the method of moving axes, as defined in the first chapter, has been extended so as to be applicable to an investigation of the properties of surfaces and groups of surfaces. The extent of the theory concerning ordinary points is so great that no attempt has been made to consider the exceptional problems. For a discussion of such questions as the existence of integrals of differential equations and boundary conditions the reader must consult the treatises which deal particularly with these subjects. In Chapters VII and VIII the theory previously developed is applied to several groups of surfaces, such as the quadrics, ruled surfaces, minimal surfaces, surfaces of constant total curvature, and surfaces with plane and spherical lines of curvature. 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.

Author : Luther Pfahler Eisenhart
Publisher : Literary Licensing, LLC
Page : 490 pages
File Size : 52,5 Mb
Release : 2014-08-07
Category : Electronic
ISBN : 1498137369

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A Treatise on the Differential Geometry of Curves and Surfaces (1909) by Luther Pfahler Eisenhart Pdf

This Is A New Release Of The Original 1909 Edition.

Author : Luther Pfahler Eisenhart
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 1960
Category : Geometry, Differential
ISBN : LCCN:cvx00008951

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A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart Pdf

Author : Forsyth Andrew Russell
Publisher : Wentworth Press
Page : 550 pages
File Size : 48,5 Mb
Release : 2019-02-28
Category : History
ISBN : 0526320575

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Lectures on the Differential Geometry of Curves and Surfaces by Forsyth Andrew Russell Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : E. J. Wilczynski
Publisher : Forgotten Books
Page : 312 pages
File Size : 52,5 Mb
Release : 2017-10-22
Category : Mathematics
ISBN : 0266589561

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Projective Differential Geometry of Curves and Ruled Surfaces (Classic Reprint) by E. J. Wilczynski Pdf

Excerpt from Projective Differential Geometry of Curves and Ruled Surfaces The examples collected at the end of each chapter are of two kinds. Some of them are mere exercises. Some, however, (those marked with an asterisk), are of a very different nature. They are essentially suggestions for such further investigations, as appear to me to be of promise and importance. I have, also in the body of the book, taken the privilege of pointing out further problems which seem to be of interest. Many others will readily suggest themselves. It is my sincere wish that these suggestions may be helpful toward a further development of this fascinating subject. 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.

Author : Georges Valiron
Publisher : Unknown
Page : 288 pages
File Size : 55,9 Mb
Release : 1986
Category : Mathematics
ISBN : 0915692392

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The Classical Differential Geometry of Curves and Surfaces by Georges Valiron Pdf

Author : Phil Dyke
Publisher : John Wiley & Sons
Page : 400 pages
File Size : 55,9 Mb
Release : 2018-03-02
Category : Mathematics
ISBN : 9781119221791

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Two and Three Dimensional Calculus by Phil Dyke Pdf

Covers multivariable calculus, starting from the basics and leading up to the three theorems of Green, Gauss, and Stokes, but always with an eye on practical applications. Written for a wide spectrum of undergraduate students by an experienced author, this book provides a very practical approach to advanced calculus—starting from the basics and leading up to the theorems of Green, Gauss, and Stokes. It explains, clearly and concisely, partial differentiation, multiple integration, vectors and vector calculus, and provides end-of-chapter exercises along with their solutions to aid the readers’ understanding. Written in an approachable style and filled with numerous illustrative examples throughout, Two and Three Dimensional Calculus: with Applications in Science and Engineering assumes no prior knowledge of partial differentiation or vectors and explains difficult concepts with easy to follow examples. Rather than concentrating on mathematical structures, the book describes the development of techniques through their use in science and engineering so that students acquire skills that enable them to be used in a wide variety of practical situations. It also has enough rigor to enable those who wish to investigate the more mathematical generalizations found in most mathematics degrees to do so. Assumes no prior knowledge of partial differentiation, multiple integration or vectors Includes easy-to-follow examples throughout to help explain difficult concepts Features end-of-chapter exercises with solutions to exercises in the book. Two and Three Dimensional Calculus: with Applications in Science and Engineering is an ideal textbook for undergraduate students of engineering and applied sciences as well as those needing to use these methods for real problems in industry and commerce.

Author : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 48,8 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780817644024

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Differential Geometry of Curves and Surfaces by Victor Andreevich Toponogov Pdf

Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels

Author : R. H. Fowler
Publisher : Forgotten Books
Page : 114 pages
File Size : 53,9 Mb
Release : 2018-01-05
Category : Mathematics
ISBN : 0428367755

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The Elementary Differential Geometry of Plane Curves (Classic Reprint) by R. H. Fowler Pdf

Excerpt from The Elementary Differential Geometry of Plane Curves A limited selection of examples is given at the ends of the chapters. Besides their more Obvious function, these are intended to provide a summary of some of the more important extensions of the theorems proved in the text. References or sketches of a proof are therefore given in such cases, which should enable the reader to complete the proofs. 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.

Author : J. Hymers
Publisher : Forgotten Books
Page : 356 pages
File Size : 51,5 Mb
Release : 2017-12-15
Category : Mathematics
ISBN : 0332846512

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A Treatise on Analytical Geometry of Tree Dimensions by J. Hymers Pdf

Excerpt from A Treatise on Analytical Geometry of Tree Dimensions: Containing the Theory of Curve Surfaces, and of Curves of Double Curvature 53 - 65. Equations and forms of surfaces that have a center 66 - 72. Equations and forms of surfaces that have not a. 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.

Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 54,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839881

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Differential Geometry by Wolfgang Kühnel Pdf

Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.

Author : Dirk J. Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 51,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138183

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Lectures on Classical Differential Geometry by Dirk J. Struik Pdf

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.