Elementary Geometry of Differentiable Curves

ISBN-13: 9780521804530 / Angielski / Twarda / 2001 / 238 str.

Chris Gibson; C. G. Gibson

Opis

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.

Recenzje

'It is meant to be a genuine introduction to the differential geometry of plane curves and in fact it is … I can warmly recommend this booklet for students and scientists who have not yet gathered experience in differential geometry and who want to give themselves a treat.' J. Lang, IMN (Internationale Mathematische Nachrichten)

Spis treści

1. The Euclidean plane; 2. Parametrized curves; 3. Classes of special curves; 4. Arc length; 5. Curvature; 6. Existence and uniqueness; 7. Contact with lines; 8. Contact with circles; 9. Vertices; 10. Envelopes; 11. Orthotomics; 12. Caustics by reflexion; 13. Planar kinematics; 14. Centrodes; 15. Geometry of trajectories.