03933nam a22005055i 4500 978-3-319-01736-5 DE-He213 20210618001725.0 cr nn 008mamaa 131108s2014 gw | s |||| 0|eng d 9783319017365 978-3-319-01736-5 10.1007/978-3-319-01736-5 doi QA440-699 PBM bicssc MAT012000 bisacsh PBM thema 516 23 Borceux, Francis. author. aut http://id.loc.gov/vocabulary/relators/aut A Differential Approach to Geometry [electronic resource] : Geometric Trilogy III / by Francis Borceux. 1st ed. 2014. Cham : Springer International Publishing : Imprint: Springer, 2014. XVI, 452 p. 159 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. Geometry. Differential geometry. Mathematics. History. Geometry. https://scigraph.springernature.com/ontologies/product-market-codes/M21006 Differential Geometry. https://scigraph.springernature.com/ontologies/product-market-codes/M21022 History of Mathematical Sciences. https://scigraph.springernature.com/ontologies/product-market-codes/M23009 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783319017358 Printed edition: 9783319017372 Printed edition: 9783319377476 https://doi.org/10.1007/978-3-319-01736-5 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)