Differential Geometry of Curves and Surfaces
Chapman & Hall/CRC (Verlag)
978-1-032-91998-0 (ISBN)
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.
Thomas F. Banchoff is a geometer and a professor at Brown University. Dr. Banchoff was president of the Mathematical Association of America (MAA) from 1999 to 2000. He has published numerous papers in a variety of journals and has been the recipient of many honors, including the MAA’s Deborah and Franklin Tepper Haimo Award and Brown’s Teaching with Technology Award. He is the author of several books, including Linear Algebra Through Geometry with John Wermer and Beyond the Third Dimension. Stephen T. Lovett is an associate professor of mathematics at Wheaton College. Dr. Lovett has taught introductory courses on differential geometry for many years, including at Eastern Nazarene College. He has given many talks over the past several years on differential and algebraic geometry as well as cryptography. In 2015, he was awarded Wheaton’s Senior Scholarship Faculty Award. He is the author of Abstract Algebra: Structures and Applications and Differential Geometry of Manifolds.
Plane Curves: Local Properties. Plane Curves: Global Properties. Curves in Space: Local Properties. Curves in Space: Global Properties. Regular Surfaces. The First and Second Fundamental Forms. The Fundamental Equations of Surfaces. The Gauss–Bonnet Theorem and Geometry of Geodesics. Curves and Surfaces in n-Dimensional Euclidean Space. Appendix.
| Erscheinungsdatum | 16.10.2024 |
|---|---|
| Zusatzinfo | 89 Illustrations, black and white |
| Sprache | englisch |
| Maße | 191 x 235 mm |
| Gewicht | 793 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-032-91998-1 / 1032919981 |
| ISBN-13 | 978-1-032-91998-0 / 9781032919980 |
| Zustand | Neuware |
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