Elementary Geometry of Differentiable Curves
An Undergraduate Introduction
216 pages, parution le 01/05/2001
Résumé
This genuine introduction to the differential geometry of
plane curves is designed as a first text for undergraduates
in mathernatics, 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 via the central
concepts of evolute and orthotomic. The final chapters
introduce the core material of classical kînematics,
developing the geometry of trajectories via the ideas of
roulettes and centrodes, and culminatîng in the inflexion
circle and cubic of stationary curvature.
Contents
- 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
- Geomerty of Trajectories
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Cambridge University Press |
| Auteur(s) | C.G. Gibson |
| Parution | 01/05/2001 |
| Nb. de pages | 216 |
| Format | 15 x 22,8 |
| Couverture | Broché |
| Poids | 339g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780521011075 |
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