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Author : Michael Spivak
Publisher : Unknown
Page : 702 pages
File Size : 51,6 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015062882942
Author : Michael Spivak
Publisher : Unknown
Page : 733 pages
File Size : 40,7 Mb
Release : 2010
Category : Mechanics
ISBN : 0914098322
Author : T. J. Willmore
Publisher : Courier Corporation
Page : 336 pages
File Size : 53,5 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486282107
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205418
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Author : Andrei Agrachev,Davide Barilari,Ugo Boscain
Publisher : Cambridge University Press
Page : 765 pages
File Size : 40,5 Mb
Release : 2019-10-31
Category : Mathematics
ISBN : 9781108476355
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 42,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387217529
Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Author : Michael Spivak
Publisher : Hachette UK
Page : 177 pages
File Size : 40,8 Mb
Release : 1971-01-22
Category : Science
ISBN : 9780813346120
This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
Author : Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 47,8 Mb
Release : 1999
Category : Geometry, Differential
ISBN : 9780821813850
This book is based on lectures given at Harvard University during the academic year 1960-1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. His reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.
Author : Gerard Walschap
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 54,8 Mb
Release : 2012-08-23
Category : Mathematics
ISBN : 9780387218267
This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.
Author : Michael Spivak
Publisher : Unknown
Page : 474 pages
File Size : 47,6 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:488789978
Author : Troy L Story
Publisher : iUniverse
Page : 165 pages
File Size : 45,6 Mb
Release : 2005
Category : Geometry, Differential
ISBN : 9780595339211
Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.
Author : Barrett O'Neill
Publisher : Academic Press
Page : 422 pages
File Size : 52,5 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268118
Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.
Author : Jeffrey M. Lee
Publisher : American Mathematical Society
Page : 671 pages
File Size : 49,6 Mb
Release : 2022-03-08
Category : Mathematics
ISBN : 9781470469825
Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.
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
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 : John Snygg
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 53,5 Mb
Release : 2011-12-09
Category : Mathematics
ISBN : 9780817682835
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
