Umfang:
Online-Ressource (XVI, 452 p. 159 illus, online resource)
ISBN:
9783319017365
Serie:
SpringerLink
Inhalt:
Introduction -- Preface -- 1.The Genesis of Differential Methods -- 2.Plane Curves -- 3.A Museum of Curves -- 4.Skew Curves -- 5.Local Theory of Surfaces -- 6.Towards Riemannian Geometry -- 7.Elements of Global Theory of Surfaces -- Appendices: A.Topology -- B.Differential Equations -- Index -- Bibliography
Inhalt:
This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providing an integrated presentation fully accessible to undergraduate-level students. At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions, not just those constructed from polynomials. During the 18th century, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter this fascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincaré characteristics) associated with a surface gives you a lot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry, the geometry that underlies the theory of relativity. The book is of interest to all those who teach classical differential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to “intuitively” introduce students to the highly technical nature of this branch of mathematics, in particular when preparing students for courses on relativity
Anmerkung:
Includes bibliographical references and index
,
IntroductionPreface -- 1.The Genesis of Differential Methods -- 2.Plane Curves -- 3.A Museum of Curves -- 4.Skew Curves -- 5.Local Theory of Surfaces -- 6.Towards Riemannian Geometry -- 7.Elements of Global Theory of Surfaces -- Appendices: A.Topology -- B.Differential Equations -- Index -- Bibliography.
Weitere Ausg.:
ISBN 9783319017358
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Borceux, Francis, 1948 - Geometric trilogy ; 3: A differential approach to geometry Cham : Springer, 2014 ISBN 9783319017358
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Borceux, Francis, 1948 - Geometric trilogy ; 3: An differential approach to geometry Cham [u.a.] : Springer, 2014 ISBN 9783319017358
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Differentialgeometrie
DOI:
10.1007/978-3-319-01736-5
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Borceux, Francis 1948-
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