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Author : Lyndon Woodward,John Bolton
Publisher : Cambridge University Press
Page : 275 pages
File Size : 40,8 Mb
Release : 2019
Category : Mathematics
ISBN : 9781108424936
With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.
Author : Thierry Aubin
Publisher : American Mathematical Soc.
Page : 198 pages
File Size : 46,8 Mb
Release : 2001
Category : Geometry, Differential
ISBN : 9780821827093
This textbook for second-year graduate students is intended as an introduction to differential geometry with principal emphasis on Riemannian geometry. Chapter I explains basic definitions and gives the proofs of the important theorems of Whitney and Sard. Chapter II deals with vector fields and differential forms. Chapter III addresses integration of vector fields and p-plane fields. Chapter IV develops the notion of connection on a Riemannian manifold considered as a means to define parallel transport on the manifold. The author also discusses related notions of torsion and curvature, and gives a working knowledge of the covariant derivative. Chapter V specializes on Riemannian manifolds by deducing global properties from local properties of curvature, the final goal being to determine the manifold completely. Chapter VI explores some problems in PDEs suggested by the geometry of manifolds. The author is well-known for his significant contributions to the field of geometry and PDEs - particularly for his work on the Yamabe problem - and for his expository accounts on the subject. The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.
Author : Anonim
Publisher : Unknown
Page : 343 pages
File Size : 48,9 Mb
Release : 1997
Category : Geometry, Differential
ISBN : 1571462805
Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 51,6 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780817681227
The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.
Author : W. Klingenberg
Publisher : Springer Science & Business Media
Page : 188 pages
File Size : 51,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781461299233
This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin ary differential equations are Hurewicz, W. Lectures on ordinary differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, New York, 1977. Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some e1aborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour. 1 wish to thank David for his work and his enthusiasm during the whole period of our collaboration. At the same time I would like to commend the editors of Springer-Verlag for their patience and good advice. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German Edition This book has its origins in a one-semester course in differential geometry which 1 have given many times at Gottingen, Mainz, and Bonn.
Author : Dorairaj Somasundaram
Publisher : Alpha Science Int'l Ltd.
Page : 472 pages
File Size : 54,7 Mb
Release : 2005
Category : Computers
ISBN : 184265182X
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.
Author : Izu Vaisman
Publisher : CRC Press
Page : 184 pages
File Size : 52,7 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000110555
This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.
Author : Andrew McInerney
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 53,8 Mb
Release : 2013-07-09
Category : Mathematics
ISBN : 9781461477327
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
Author : Chuan-Chih Hsiung
Publisher : International Press of Boston
Page : 376 pages
File Size : 48,5 Mb
Release : 1997
Category : Mathematics
ISBN : UOM:39015047056901
This textbook on differential geometry is designed for graduate and undergraduate students. It covers both curves and surfaces in three-dimensional education space but can be extended to higher dimensions and other surfaces. It can be used for either one semester or a full-year course.
Author : S. Kumaresan
Publisher : Springer
Page : 306 pages
File Size : 43,5 Mb
Release : 2002-01-15
Category : Mathematics
ISBN : 9789386279088
Author : Izu Vaisman
Publisher : CRC Press
Page : 186 pages
File Size : 55,6 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000146400
This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.
Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 50,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781447136965
Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.
Author : Lawrence Conlon
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 46,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475722840
This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.
Author : D. Somasundaram
Publisher : Unknown
Page : 468 pages
File Size : 47,5 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8173195463
Author : Walter A. Poor
Publisher : Courier Corporation
Page : 352 pages
File Size : 51,7 Mb
Release : 2015-04-27
Category : Mathematics
ISBN : 9780486151915
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
