Differential Geometry of Curves and Surfaces
Thomas F Banchoff author Stephen T Lovett author
Format:Hardback
Publisher:Taylor & Francis Inc
Published:10th Sep '15
Currently unavailable, and unfortunately no date known when it will be back
Differential Geometry of Curves and Surfaces, Second Edition takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive computer graphics applets supported by sound theory.
The book explains the reasons for various definitions while the interactive applets offer motivation for certain definitions, allow students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits.
New to the Second Edition
- Reworked presentation to make it more approachable
- More exercises, both introductory and advanced
- New section on the application of differential geometry to cartography
- Additional investigative project ideas
- Significantly reorganized material on the Gauss–Bonnet theorem
- Two new sections dedicated to hyperbolic and spherical geometry as applications of intrinsic geometry
- A new chapter on curves and surfaces in Rn
Suitable for an undergraduate-level course or self-study, this self-contained textbook and online software applets provide students with a rigorous yet intuitive introduction to the field of differential geometry. The text gives a detailed introduction of definitions, theorems, and proofs and includes many types of exercises appropriate for daily or weekly assignments. The applets can be used for computer labs, in-class illustrations, exploratory exercises, or self-study aids.
Praise for the First Edition:"… a complete guide for the study of classical theory of curves and surfaces and is intended as a textbook for a one-semester course for undergraduates …The main advantages of the book are the careful introduction of the concepts, the good choice of the exercises, and the interactive computer graphics, which make the text well-suited for self-study. …The access to online computer graphics applets that illustrate many concepts and theorems presented in the text provides the readers with an interesting and visually stimulating study of classical differential geometry. … I strongly recommend [this book and Differential Geometry of Manifolds] to anyone wishing to enter into the beautiful world of the differential geometry."
—Velichka Milousheva, Journal of Geometry and Symmetry in Physics, 2012
"Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book … Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena."
—L’Enseignement Mathématique (2) 57 (2011)
"… an intuitive and visual introduction to the subject is beneficial in an undergraduate course. This attitude is reflected in the text. The authors spent quite some time on motivating particular concepts and discuss simple but instructive examples. At the same time, they do not neglect rigour and precision. … As a distinguishing feature to other textbooks, there is an accompanying web page containing numerous interactive Java applets. … The applets are well-suited for use in classroom teaching or as an aid to self-study."
—Hans-Peter Schröcker, Zentralblatt MATH 1200
"Coming from intuitive considerations to precise definitions the authors have written a very readable book. Every section contains many examples, problems and figures visualizing geometric properties. The understanding of geometric phenomena is supported by a number of available Java applets. This special feature distinguishes the textbook from others and makes it recommendable for self studies too. … highly recommendable …"
—F. Manhart, International Mathematical News, August 2011
"… the authors succeeded in making this modern view of differential geometry of curves and surfaces an approachable subject for advanced undergraduates."
—Andrew Bucki, Mathematical Reviews, Issue 2011h
"… an essential addition to academic library mathematical studies instructional reference collections, as well as an ideal classroom textbook."
—Midwest Book Review, May 2011
ISBN: 9781482247343
Dimensions: unknown
Weight: 960g
432 pages
2nd edition