elementary topics in differential geometry

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Elementary Topics In Differential Geometry

Author : J. A. Thorpe
ISBN : 9781461261537
Genre : Mathematics
File Size : 63. 83 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.

Elementary Topics In Differential Geometry

Author : John A. Thorpe
ISBN : 3540903577
Genre : Differentialgeometrie
File Size : 88. 57 MB
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Elementary Topics In Differential Geometry

Author : John A. Thorpe
ISBN : OCLC:46990376
Genre : Geometry, Differential
File Size : 88. 60 MB
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Elementare Differentialgeometrie

Author : Christian Bär
ISBN : 9783110224597
Genre : Mathematics
File Size : 81. 88 MB
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This textbook presents an introduction to the differential geometry of curves and surfaces. This second, revised edition has been expanded to include solutions and applications in cartography. Topics include Euclidean geometry, curve theory, surface theory, curvature concepts, minimal surfaces, Riemann geometry and the Gauss-Bonnet theorem.

Differentialgeometrie Von Kurven Und Fl Chen

Author : Manfredo P. do Carmo
ISBN : 9783322850720
Genre : Technology & Engineering
File Size : 63. 63 MB
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Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Topics In Differential Geometry A New Approach Using D Differentiation

Author : Donal J. Hurley
ISBN : 1852334916
Genre : Mathematics
File Size : 66. 23 MB
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This book is the first comprehensive and self-contained treatment of the new concept of D-differentiation aimed primarily at advanced graduate students and researchers in the fields of differential geometry, mathematics and mathematical physics.

Differential Geometry Of Curves And Surfaces

Author : Kristopher Tapp
ISBN : 9783319397993
Genre : Mathematics
File Size : 76. 64 MB
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This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.

Elementary Differential Geometry Revised 2nd Edition

Author : Barrett O'Neill
ISBN : 0080505422
Genre : Mathematics
File Size : 45. 78 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 : A.N. Pressley
ISBN : 9781848828919
Genre : Mathematics
File Size : 36. 71 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

Author : Christian Bär
ISBN : 9780521896719
Genre : Mathematics
File Size : 27. 47 MB
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This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.

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