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Author : Eisenhart Luther Pfahler
Publisher :
ISBN 13 : 9780243847754
Total Pages : pages
Book Rating : 4.8/5 (477 download)
Download or read book Treatise On the Differential Geometry of Curves and Surfaces written by Eisenhart Luther Pfahler and published by . This book was released on 1901 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Luther Pfahler Eisenhart
Publisher :
ISBN 13 :
Total Pages : 474 pages
Book Rating : 4.:/5 (312 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1965 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Luther Pfahler Eisenhart
Publisher :
ISBN 13 :
Total Pages : 524 pages
Book Rating : 4.:/5 (4 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1909 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart, first published in 1909, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Author : Luther Pfahler Eisenhart
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 ( download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1960 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shoshichi Kobayashi
Publisher : Springer Nature
ISBN 13 : 9811517398
Total Pages : 192 pages
Book Rating : 4.8/5 (115 download)
Download or read book Differential Geometry of Curves and Surfaces written by Shoshichi Kobayashi and published by Springer Nature. This book was released on 2019-11-13 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces. Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature K and the mean curvature H —are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain. Then the Gauss–Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number χ(S). Here again, many illustrations are provided to facilitate the reader’s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.
Author : Luther Pfahler Eisenhart
Publisher : Forgotten Books
ISBN 13 : 9781528484626
Total Pages : 490 pages
Book Rating : 4.4/5 (846 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces (Classic Reprint) written by Luther Pfahler Eisenhart and published by Forgotten Books. This book was released on 2017-09-18 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Masaaki Umehara
Publisher : World Scientific Publishing Company
ISBN 13 : 9814740268
Total Pages : 327 pages
Book Rating : 4.8/5 (147 download)
Download or read book Differential Geometry Of Curves And Surfaces written by Masaaki Umehara and published by World Scientific Publishing Company. This book was released on 2017-05-12 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.
Author : Luther Pfahler Eisenhart
Publisher : Literary Licensing, LLC
ISBN 13 : 9781498137362
Total Pages : 490 pages
Book Rating : 4.1/5 (373 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces (1909) written by Luther Pfahler Eisenhart and published by Literary Licensing, LLC. This book was released on 2014-08-07 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Is A New Release Of The Original 1909 Edition.
Author : Eisenhart Luther Pfahler 1876, B.
Publisher : Hardpress Publishing
ISBN 13 : 9781313261135
Total Pages : 498 pages
Book Rating : 4.2/5 (611 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Eisenhart Luther Pfahler 1876, B. and published by Hardpress Publishing. This book was released on 2013-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Author : Thomas F. Banchoff
Publisher : CRC Press
ISBN 13 : 1568814569
Total Pages : 349 pages
Book Rating : 4.5/5 (688 download)
Download or read book Differential Geometry of Curves and Surfaces written by Thomas F. Banchoff and published by CRC Press. This book was released on 2010-03-01 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
Author : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
ISBN 13 : 0817644024
Total Pages : 215 pages
Book Rating : 4.8/5 (176 download)
Download or read book Differential Geometry of Curves and Surfaces written by Victor Andreevich Toponogov and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Luther Pfahler Eisenhart (né)
Publisher :
ISBN 13 :
Total Pages : 474 pages
Book Rating : 4.:/5 (422 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart (né) and published by . This book was released on 1960 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
ISBN 13 : 0821839888
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)
Download or read book Differential Geometry written by Wolfgang Kühnel and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Thomas F. Banchoff
Publisher : CRC Press
ISBN 13 : 100059775X
Total Pages : 371 pages
Book Rating : 4.0/5 (5 download)
Download or read book Differential Geometry of Curves and Surfaces written by Thomas F. Banchoff and published by CRC Press. This book was released on 2022-08-05 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through two previous editions, the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format, which readers can access using the free Maple Player. The book explains the reasons for various definitions while the interactive applets offer motivation for definitions, allowing students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research. At users of the previous editions' request, this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises. This student-friendly and readable approach offers additional examples, well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem, the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also, the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms.
Author : Luther Pfahler Eisenhart
Publisher : Nabu Press
ISBN 13 : 9781294667988
Total Pages : 496 pages
Book Rating : 4.6/5 (679 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces - Primary Source Edition written by Luther Pfahler Eisenhart and published by Nabu Press. This book was released on 2014-02-22 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Author : Manfredo Perdigão do Carmo
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 522 pages
Book Rating : 4.F/5 ( download)
Download or read book Differential Geometry of Curves and Surfaces written by Manfredo Perdigão do Carmo and published by Prentice Hall. This book was released on 1976 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers local as well as global differential geometry of curves and surfaces.
Author : Dorairaj Somasundaram
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9781842651827
Total Pages : 472 pages
Book Rating : 4.6/5 (518 download)
Download or read book Differential Geometry written by Dorairaj Somasundaram and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry: A First Course is an introduction to the classical theory of space curves and surfaces offered in graduate and postgraduate courses in mathematics. Based on Serret-Frenet formulae, the theory of space curves is developed and concluded with a detailed discussion on fundamental existence theorem. The theory of surfaces includes the first fundamental form with local intrinsic properties, geodesics on surfaces, the second fundamental form with local non-intrinsic properties and the fundamental equations of the surface theory with several applications.
