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 : 26. 19 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 Revised 2nd Edition

Author : CTI Reviews
ISBN : 9781478417712
Genre : Education
File Size : 76. 67 MB
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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.

Elementary Differential Geometry

Author : Barrett O'Neill
ISBN : 9781483268118
Genre : Mathematics
File Size : 39. 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 : 78. 26 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>

Lectures On Classical Differential Geometry

Author : Dirk Jan Struik
ISBN : 0486656098
Genre : Mathematics
File Size : 50. 37 MB
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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.

Modern Differential Geometry Of Curves And Surfaces With Mathematica Third Edition

Author : Elsa Abbena
ISBN : 1584884487
Genre : Mathematics
File Size : 68. 42 MB
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Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

Differential Geometry Of Curves And Surfaces

Author : Manfredo P. do Carmo
ISBN : 9780486806990
Genre : Mathematics
File Size : 76. 68 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.

Lecture Notes On Elementary Topology And Geometry

Author : I.M. Singer
ISBN : 0387902023
Genre : Mathematics
File Size : 45. 78 MB
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At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.

Recent Progress In Differential Geometry And Its Related Fields

Author : Toshiaki Adachi
ISBN : 9789814355469
Genre : Mathematics
File Size : 40. 97 MB
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This volume contains the contributions by the main participants of the 2nd International Colloquium on Differential Geometry and its Related Fields (ICDG2010), held in Veliko Tarnovo, Bulgaria to exchange information on current topics in differential geometry, information geometry and applications. These contributions from active specialists in differential geometry provide significant information on research papers which cover geometric structures, concrete Lie group theory and information geometry. This volume is invaluable not only for researchers in this special area but also for those who are interested in interdisciplinary areas in differential geometry, complex analysis, probability theory and mathematical physics. It also serves as a good guide to graduate students in the field of differential geometry.

Curvature In Mathematics And Physics

Author : Shlomo Sternberg
ISBN : 9780486478555
Genre : Mathematics
File Size : 24. 29 MB
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As astronaut Donald K. Slayton notes in his Foreword, this chronicle emphasizes the cooperation of "humans on space and on the ground. It realistically balances the role of the highly visible astronaut with the mammoth supporting team." An official NASA publication, Suddenly, Tomorrow Came is profusely illustrated with forty-four figures and tables, plus sixty-three photographs. Historian Paul Dickson brings the narrative up to date with an informative new Introduction.

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