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Elementary Geometry of Differentiable Curves : An Undergraduate Introduction by C. G. Gibson (2001, Trade Paperback)
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521011078
ISBN-139780521011075
eBay Product ID (ePID)1933412
Product Key Features
Number of Pages238 Pages
Publication NameElementary Geometry of Differentiable Curves : an Undergraduate Introduction
LanguageEnglish
SubjectGeometry / Differential, Topology, Geometry / Algebraic
Publication Year2001
TypeTextbook
AuthorC. G. Gibson
Subject AreaMathematics
FormatTrade Paperback
Dimensions
Item Height0.7 in
Item Weight12 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceCollege Audience
LCCN2002-276146
Dewey Edition21
Reviews'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), "This book is pleasant for a student...It contains many interesting properties and features of curves which usually are not shown in a regular undergraduate course." Mathematical Reviews, '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)
IllustratedYes
Dewey Decimal516.3/6
Table Of Content1. 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.
SynopsisThis genuine introduction to the differential geometry of plane curves is designed as an adoptable course text for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. It assumes only foundational year mathematics, and is well illustrated with several hundred worked examples and exercises., 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., This 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 via the central concepts of evolute and orthotomic. The final chapters introduce 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.
LC Classification NumberQA643 .G53 2001
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