A Treatise On The Differential Geometry Of Curves And Surfaces
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A Treatise On The Differential Geometry Of Curves And Surfaces
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Courier Corporation
Release Date : 2013-04-25
A Treatise On The Differential Geometry Of Curves And Surfaces written by Luther Pfahler Eisenhart and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-25 with Mathematics categories.
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.
Treatise On The Differential Geometry Of Curves And Surfaces
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Author : LUTHER PFAHLER. EISENHART
language : en
Publisher:
Release Date : 2019
Treatise On The Differential Geometry Of Curves And Surfaces written by LUTHER PFAHLER. EISENHART and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
A Treatise On The Differential Geometry Of Curves And Surfaces Classic Reprint
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Forgotten Books
Release Date : 2017-09-18
A Treatise On The Differential Geometry Of Curves And Surfaces Classic Reprint written by Luther Pfahler Eisenhart and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-18 with Mathematics categories.
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.
A Treatise On The Differential Geometry Of Curves And Surfaces 1909
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Literary Licensing, LLC
Release Date : 2014-08-07
A Treatise On The Differential Geometry Of Curves And Surfaces 1909 written by Luther Pfahler Eisenhart and has been published by Literary Licensing, LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-07 with categories.
This Is A New Release Of The Original 1909 Edition.
A Treatise On The Differential Geometry Of Curves And Surfaces
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Forgotten Books
Release Date : 2015-06-15
A Treatise On The Differential Geometry Of Curves And Surfaces written by Luther Pfahler Eisenhart and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-15 with Mathematics categories.
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.
A Treatise On The Differential Geometry Of Curves And Surfaces
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Author : Luther Pfahler Eisenhart
language : en
Publisher:
Release Date : 1960
A Treatise On The Differential Geometry Of Curves And Surfaces written by Luther Pfahler Eisenhart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Geometry, Differential categories.
Introduction To Differential Geometry Of Space Curves And Surfaces
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Author : Taha Sochi
language : en
Publisher: Lulu.com
Release Date :
Introduction To Differential Geometry Of Space Curves And Surfaces written by Taha Sochi and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Differential Geometry Of Curves And Surfaces
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Author : Manfredo P. do Carmo
language : en
Publisher: Courier Dover Publications
Release Date : 2016-12-14
Differential Geometry Of Curves And Surfaces written by Manfredo P. do Carmo and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-14 with Mathematics categories.
One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.
Differential Geometry Of Curves And Surfaces
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Author : Kristopher Tapp
language : en
Publisher: Springer
Release Date : 2016-09-30
Differential Geometry Of Curves And Surfaces written by Kristopher Tapp and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-30 with Mathematics categories.
This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.
Differential Geometry Of Curves And Surfaces
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Author : Manfredo Perdigão do Carmo
language : en
Publisher: Prentice Hall
Release Date : 1976
Differential Geometry Of Curves And Surfaces written by Manfredo Perdigão do Carmo and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
This volume covers local as well as global differential geometry of curves and surfaces.