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Elementary Geometry of Differentiable Curves An Undergraduate Introduction

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ISBN-10: 0521011078

ISBN-13: 9780521011075

Edition: 2001

Authors: C. G. Gibson

List price: $78.99
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Description:

Here is a genuine introduction to the differential geometry of plane curves for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. This well-illustrated text contains several hundred worked examples and exercises, making it suitable for adoption as a course text. Key concepts are illustrated by named curves, of historical and scientific significance, leading to the central idea of curvature. The author introduces the core material of classical kinematics, developing the geometry of trajectories via the ideas of roulettes and centrodes, and culminating in the inflexion circle and cubic of stationary curvature.
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Book details

List price: $78.99
Copyright year: 2001
Publisher: Cambridge University Press
Publication date: 5/17/2001
Binding: Paperback
Pages: 238
Size: 5.98" wide x 9.02" long x 0.67" tall
Weight: 0.748
Language: English

Chris Gibson received an honours degree in Mathematics from St Andrews University in 1963, and later the degrees of Drs Math and Dr Math from the University of Amsterdam, returning to England in 1967 to begin his 35 year mathematics career at the University of Liverpool. His interests turned towards the geometric areas, and he was a founder member of the Liverpool Singularities Group until his retirement in 2002 as Reader in Pure Mathematics, with over 60 published papers in that area. In 1974 he co-authored the significant 'Topological Stability of Smooth Mappings' (published by Springer Verlag) presenting the first detailed proof of Thom's Topological Stability Theorem. In addition to…    

The Euclidean plane
Parametrized curves
Classes of special curves
Arc length
Curvature
Existence and uniqueness
Contact with lines
Contact with circles
Vertices
Envelopes
Orthotomics
Caustics by reflexion
Planar kinematics
Centrodes
Geometry of trajectories