Elementary Geometry of Differentiable Curves An Undergraduate Introduction

Elementary Geometry of Differentiable CurvesAn Undergraduate Introduction\nAuthor(s): C. G. Gibson\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521804530, 978-0521804530\nSynopsis\nThis genuine introduction to the differential geometry of plane curves is designed as a first text for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. The book assumes only foundational year mathematics: it is well illustrated, and contains several hundred worked examples and exercises, making it suitable for adoption as a course text. The basic concepts are illustrated by named curves, of historical and scientific significance, leading to the central idea of curvature. The singular viewpoint is represented by a study of contact with lines and circles, illuminating the ideas of cusp, inflexion and vertex. There are two major physical applications. Caustics are discussed v.