Elementary Differential Geometry

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Elementary Differential Geometry

A.N. Pressley
Elementary Differential Geometry Book PDF

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 47,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781447136965

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Elementary Differential Geometry by A.N. Pressley Pdf

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.

Elementary Differential Geometry

Barrett O'Neill
Elementary Differential Geometry Book PDF

Author : Barrett O'Neill
Publisher : Academic Press
Page : 422 pages
File Size : 53,8 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268118

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Elementary Differential Geometry by Barrett O'Neill Pdf

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

A.N. Pressley
Elementary Differential Geometry Book PDF

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 474 pages
File Size : 44,9 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9781848828919

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Elementary Differential Geometry by A.N. Pressley Pdf

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 Topics in Differential Geometry

J. A. Thorpe
Elementary Topics in Differential Geometry Book PDF

Author : J. A. Thorpe
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261537

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Elementary Topics in Differential Geometry by J. A. Thorpe Pdf

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.

Elementary Differential Geometry

Christian Bär
Elementary Differential Geometry Book PDF

Author : Christian Bär
Publisher : Cambridge University Press
Page : 335 pages
File Size : 46,5 Mb
Release : 2010-05-06
Category : Mathematics
ISBN : 9780521896719

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Elementary Differential Geometry by Christian Bär Pdf

This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Hung Nguyen-Schäfer,Jan-Philip Schmidt
Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers Book PDF

Author : Hung Nguyen-Schäfer,Jan-Philip Schmidt
Publisher : Springer
Page : 389 pages
File Size : 40,9 Mb
Release : 2016-08-16
Category : Technology & Engineering
ISBN : 9783662484975

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Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers by Hung Nguyen-Schäfer,Jan-Philip Schmidt Pdf

This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

Differential Geometry

Heinrich W. Guggenheimer
Differential Geometry Book PDF

Author : Heinrich W. Guggenheimer
Publisher : Courier Corporation
Page : 400 pages
File Size : 49,7 Mb
Release : 2012-04-27
Category : Mathematics
ISBN : 9780486157207

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Differential Geometry by Heinrich W. Guggenheimer Pdf

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Elementary Differential Geometry

Barrett O'Neill
Elementary Differential Geometry Book PDF

Author : Barrett O'Neill
Publisher : Unknown
Page : 434 pages
File Size : 55,7 Mb
Release : 1966
Category : Mathematics
ISBN : UOM:39015015606273

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Elementary Differential Geometry by Barrett O'Neill Pdf

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

A Course in Differential Geometry

W. Klingenberg
A Course in Differential Geometry Book PDF

Author : W. Klingenberg
Publisher : Springer Science & Business Media
Page : 188 pages
File Size : 48,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781461299233

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A Course in Differential Geometry by W. Klingenberg Pdf

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.

Differential Geometry of Curves and Surfaces

Masaaki Umehara,Kotaro Yamada
Differential Geometry of Curves and Surfaces Book PDF

Author : Masaaki Umehara,Kotaro Yamada
Publisher : World Scientific Publishing Company
Page : 328 pages
File Size : 51,9 Mb
Release : 2017-05-12
Category : Electronic
ISBN : 9789814740265

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Differential Geometry of Curves and Surfaces by Masaaki Umehara,Kotaro Yamada Pdf

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

Differential Geometry of Curves and Surfaces

Shoshichi Kobayashi
Differential Geometry of Curves and Surfaces Book PDF

Author : Shoshichi Kobayashi
Publisher : Springer Nature
Page : 192 pages
File Size : 43,5 Mb
Release : 2019-11-13
Category : Mathematics
ISBN : 9789811517396

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Differential Geometry of Curves and Surfaces by Shoshichi Kobayashi Pdf

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.

Differential Geometry and Mathematical Physics

Gerd Rudolph,Matthias Schmidt
Differential Geometry and Mathematical Physics Book PDF

Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 41,8 Mb
Release : 2012-11-09
Category : Science
ISBN : 9789400753457

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Differential Geometry and Mathematical Physics by Gerd Rudolph,Matthias Schmidt Pdf

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Differential Geometry

Wolfgang Kühnel
Differential Geometry Book PDF

Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 50,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839881

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Differential Geometry by Wolfgang Kühnel Pdf

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.

The Elementary Differential Geometry of Plane Curves

Ralph Howard Fowler
The Elementary Differential Geometry of Plane Curves Book PDF

Author : Ralph Howard Fowler
Publisher : Legare Street Press
Page : 0 pages
File Size : 49,9 Mb
Release : 2022-10-27
Category : History
ISBN : 1016472412

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The Elementary Differential Geometry of Plane Curves by Ralph Howard Fowler Pdf

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 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. 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.

Differential Geometry of Curves and Surfaces

Victor Andreevich Toponogov
Differential Geometry of Curves and Surfaces Book PDF

Author : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 47,6 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780817644024

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Differential Geometry of Curves and Surfaces by Victor Andreevich Toponogov Pdf

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