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Author : Andrew Russell Forsyth
Publisher : Unknown
Page : 527 pages
File Size : 44,9 Mb
Release : 1920
Category : Electronic
ISBN : OCLC:749453375
Author : Andrew Russell Forsyth
Publisher : Hardpress Publishing
Page : 566 pages
File Size : 48,9 Mb
Release : 2012-08-01
Category : Electronic
ISBN : 1290925585
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 : Masaaki Umehara,Kotaro Yamada
Publisher : World Scientific Publishing Company
Page : 328 pages
File Size : 47,5 Mb
Release : 2017-05-12
Category : Electronic
ISBN : 9789814740265
This 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. Request Inspection Copy
Author : Forsyth Andrew Russell
Publisher : Wentworth Press
Page : 550 pages
File Size : 46,8 Mb
Release : 2019-02-28
Category : History
ISBN : 0526320575
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 : A. R. Forsyth
Publisher : Alpha Edition
Page : 556 pages
File Size : 49,5 Mb
Release : 2000-03-02
Category : History
ISBN : 9354002803
This book has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format as the same form as it was originally first published. Hence any marks or annotations seen are left intentionally to preserve its true nature.
Author : Dirk Jan Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 48,6 Mb
Release : 1961-01-01
Category : Mathematics
ISBN : 0486656098
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.
Author : Shoshichi Kobayashi
Publisher : Springer Nature
Page : 192 pages
File Size : 49,8 Mb
Release : 2019-11-13
Category : Mathematics
ISBN : 9789811517396
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 : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 44,9 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780817644024
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 : Dirk J. Struik
Publisher : Courier Corporation
Page : 254 pages
File Size : 41,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138183
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.
Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 42,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839881
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 : Manfredo Perdigão do Carmo
Publisher : Unknown
Page : 503 pages
File Size : 49,8 Mb
Release : 2004
Category : Curves
ISBN : 7111139119
责任者译名:卡莫。
Author : Manfredo P. do Carmo
Publisher : Courier Dover Publications
Page : 528 pages
File Size : 42,7 Mb
Release : 2016-12-14
Category : Mathematics
ISBN : 9780486817972
One of the most widely used texts in its field, this volume's clear, well-written exposition is enhanced by many examples and exercises, some with hints and answers. 1976 edition.
Author : Sebastián Montiel,Antonio Ros
Publisher : American Mathematical Soc.
Page : 395 pages
File Size : 50,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847633
Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.
Author : Prakash Dabhi
Publisher : Unknown
Page : 84 pages
File Size : 50,9 Mb
Release : 2015-09-01
Category : Electronic
ISBN : 3668015732
Document from the year 2015 in the subject Mathematics - Geometry, course: Differential Geometry, language: English, abstract: This is a Lecture Notes on a one semester course on Differential Geometry taught as a basic course in all M.Sc./M.S. programmes in Mathematics. This consists normally of curve theory leading up to fundamental theorem of space curves as well as the Gauss theory of surfaces covering first fundamental form, second fundamental form, Gaussian curvature, geodesic and Gauss Bonnet theorem. This Lecture Notes is based on lectures I have given to M.Sc. Mathematics students of Sardar Patel University, Vallabh Vidyanagar, India. Here are the salient features of the Lecture Notes. Proofs of all assertions are completely given in a lucid student friendly manner. A large number of solved exercises are included. All these are to facilitate self study by the students. I have also adopted the modern approach to develop the classical topics treated here. The Lecture Notes is highly influenced by the approach adopted in Elementary Differential Geometry by Andrew Pressley and Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo. I am indebted to these authors whose work have influenced my learning of the subject as well as the preparation of this Lecture Notes. I hope this little book would invite the students to the subject of Differential Geometry and would inspire them to look to some comprehensive books including those mentioned above.
Author : Masaaki Umehara,Kentaro Saji,Kotaro Yamada
Publisher : World Scientific
Page : 387 pages
File Size : 54,7 Mb
Release : 2021-11-29
Category : Mathematics
ISBN : 9789811237157
This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields — singularity theory and differential geometry.The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space. In particular, by presenting the singular curvature, which originated through research by the authors, the Gauss-Bonnet theorem for surfaces is generalized to those with singularities. The Gauss-Bonnet theorem is intrinsic in nature, that is, it is a theorem not only for surfaces but also for 2-dimensional Riemannian manifolds. The book also elucidates the notion of Riemannian manifolds with singularities.These topics, as well as elementary descriptions of proofs of the recognition theorems, cannot be found in other books. Explicit examples and models are provided in abundance, along with insightful explanations of the underlying theory as well. Numerous figures and exercise problems are given, becoming strong aids in developing an understanding of the material.Readers will gain from this text a unique introduction to the singularities of curves and surfaces from the viewpoint of differential geometry, and it will be a useful guide for students and researchers interested in this subject.
