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Titlebook: Elementary Differential Geometry; Andrew Pressley Textbook 20011st edition Springer-Verlag London 2001 Curves and Surfaces.Euclidean Geome

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书目名称Elementary Differential Geometry
编辑Andrew Pressley
视频video
概述Taking a unique approach to the subject, the book allows the reader to see some amazing results of claissical differential geometry using nothing more than basic calculus.The technical definitions are
丛书名称Springer Undergraduate Mathematics Series
图书封面Titlebook: Elementary Differential Geometry;  Andrew Pressley Textbook 20011st edition Springer-Verlag London 2001 Curves and Surfaces.Euclidean Geome
描述.Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates....Elementary Differential Geometry. presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there....The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecturers, and for all others interested in the subject....Andrew Pressley is Professor of Mathematics at King’s College London, UK....The Springer Undergraduate Mathemati
出版日期Textbook 20011st edition
关键词Curves and Surfaces; Euclidean Geometry; Gaussian curvature; Geometry; Minimal surface; curvature; differe
版次1
doihttps://doi.org/10.1007/978-1-4471-3696-5
isbn_ebook978-1-4471-3696-5Series ISSN 1615-2085 Series E-ISSN 2197-4144
issn_series 1615-2085
copyrightSpringer-Verlag London 2001
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https://doi.org/10.1007/978-3-642-98007-7In this chapter we discuss two mathematical formulations of the intuitive notion of a curve. The precise relation between them turns out to be quite subtle, so we shall begin by giving some examples of curves of each type and practical ways of passing between them.
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Curves in the Plane and in Space,In this chapter we discuss two mathematical formulations of the intuitive notion of a curve. The precise relation between them turns out to be quite subtle, so we shall begin by giving some examples of curves of each type and practical ways of passing between them.
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,Gauss’s Theorema Egregium,One of Gauss’s most important discoveries about surfaces is that the gaussian curvature is unchanged when the surface is bent without stretching. Gauss called this result ‘egregium’, and the Latin word for ‘remarkable’ has remained attached to his theorem ever since.
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Lexikon der Wirtschaftsinformatikrface patch, is all that is needed for most of the book, it does not describe adequately most of the objects that we would want to call surfaces. For example, a sphere is not a surface patch, but it can be described by gluing two surface patches together suitably. The idea behind this gluing procedu
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https://doi.org/10.1007/978-3-662-08371-0rface. Of course, this will usually be different from the distance between these points as measured by an inhabitant of the ambient three dimensional space, since the straight line segment which furnishes the shortest path between the points in .. will generally not be contained in the surface. The
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