elementary differential geometry revised 2nd edition

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Elementary Differential Geometry Revised 2nd Edition

Author : Barrett O'Neill
ISBN : 0080505422
Genre : Mathematics
File Size : 43. 36 MB
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Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text. Over 36,000 copies sold worldwide Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study Extensive update of appendices on Mathematica and Maple software packages Thorough streamlining of second edition's numbering system Fuller information on solutions to odd-numbered problems Additional exercises and hints guide students in using the latest computer modeling tools

Elementary Differential Geometry

Author : Barrett O'Neill
ISBN : 9781483268118
Genre : Mathematics
File Size : 52. 69 MB
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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.

Elementary Differential Geometry

Author : A.N. Pressley
ISBN : 9781848828919
Genre : Mathematics
File Size : 48. 4 MB
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Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul>

Elementary Differential Geometry Revised 2nd Edition

Author : CTI Reviews
ISBN : 9781478417712
Genre : Education
File Size : 25. 32 MB
Format : PDF
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Facts101 is your complete guide to Elementary Differential Geometry, Revised 2nd Edition. In this book, you will learn topics such as Euclidean Geometry, Calculus on a Surface, Shape Operators, and Geometry of Surfaces in R3 plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Differential Geometry

Author : Wolfgang Kühnel
ISBN : 9781470423209
Genre : Curves
File Size : 44. 32 MB
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This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and--as a new feature--a good number of solutions to selected exercises.

Geometry From A Differentiable Viewpoint

Author : John McCleary
ISBN : 9780521116077
Genre : Mathematics
File Size : 32. 62 MB
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A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.

Elementary Differential Geometry

Author : Barrett O'Neill
ISBN : 0125267452
Genre : Mathematics
File Size : 53. 74 MB
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Written primarily for readers who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Second Edition provides an introduction to the geometry of curves and surfaces. Although the popular First Edition has been extensively modified, this Second Edition maintains the elementary character of that volume, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis has been placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. For readers with access to the symbolic computation programs, Mathematica or Maple, the book includes approximately 30 optional computer exercises. These are not intended as an essential part of the book, but rather an extension. No computer skill is necessary to take full advantage of this comprehensive text. * Gives detailed examples for all essential ideas * Provides more than 300 exercises * Features more than 200 illustrations * Includes an introduction to using computers, and supplies answers to computer exercises given for both Mathematica and Maple systems

Differential Geometry And Its Applications

Author : John Oprea
ISBN : 0883857480
Genre : Mathematics
File Size : 59. 63 MB
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Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only “see” geodesics on surfaces, but they will also see the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

Elementary Topics In Differential Geometry

Author : J. A. Thorpe
ISBN : 9781461261537
Genre : Mathematics
File Size : 85. 99 MB
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In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.

Differential Geometry Of Curves And Surfaces

Author : Manfredo P. do Carmo
ISBN : 9780486806990
Genre : Mathematics
File Size : 28. 36 MB
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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.

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