Free Delivery Over $100
|
|
|||
|
||||
OverviewThis book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge. Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane. Full Product DetailsAuthor: Hilario Alencar , Walcy Santos , Gregorio Silva NetoPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.512kg ISBN: 9781470469597ISBN 10: 1470469596 Pages: 416 Publication Date: 30 July 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPlane curves Winding number Rotation index Jordan curve theorem Isoperimetric inequality Convex curves The four-vertex theorem Curve-shortening flow Appendix A: The class $\mathcal{C}^\infty$ convergence of the curvature function under the curve-shortening flow Appendix B: Answers to selected exercises Bibliography IndexReviewsAuthor InformationHilario Alencar, Federal University of Alagoas, Maceio, Alagoas, Brazil. Walcy Santos, Federal University of Rio de Janeiro, Brazil. Gregorio Silva Neto, Universidade Federal de Alagoas, Maceio, Alagoas, Brazil. Tab Content 6Author Website:Countries AvailableAll regions |
||||
