More New and Used
from Private Sellers
Usually Ships in 2-4 Business Days
Questions About This Book?
Why should I rent this book?
Renting is easy, fast, and cheap! Renting from eCampus.com can save you hundreds of dollars compared to the cost of new or used books each semester. At the end of the semester, simply ship the book back to us with a free UPS shipping label! No need to worry about selling it back.
How do rental returns work?
Returning books is as easy as possible. As your rental due date approaches, we will email you several courtesy reminders. When you are ready to return, you can print a free UPS shipping label from our website at any time. Then, just return the book to your UPS driver or any staffed UPS location. You can even use the same box we shipped it in!
What version or edition is this?
This is the 2nd edition with a publication date of 2/14/2010.
What is included with this book?
- The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
- The Rental copy of this book is not guaranteed to include any supplemental materials. You may receive a brand new copy, but typically, only the book itself.
Good Introduction August 17, 2011
After trying several others, I found this textbook the best for individual study. The worked out solutions to all exercises gives you a good way to check your understanding. The writing is clear and the textbook has adequate illustrations to help you see what's going on. I also liked presentation in Banchoff's book, Differential Geometry of Curves and Surfaces, but it has no answers or solutions to the exercises.
Elementary Differential Geometry: stars based on 1 user reviews.
The Springer Undergraduate Mathematics Series (SUMS) is designed for undergraduates in the mathematical sciences. From core foundational material to final year topics, SUMS books take a fresh and modern approach and are ideal for self-study or for a one- or two-semester course. Each book includes numerous examples, problems and fully-worked solutions.
Table of Contents
|Curves in the plane and in space|
|What is a curve?||p. 1|
|Closed curves||p. 19|
|Level curves versus parametrized curves||p. 23|
|How much does a curve curve?|
|Plane curves||p. 34|
|Space curves||p. 46|
|Global properties of curves|
|Simple closed curves||p. 55|
|The isoperimetric inequality||p. 58|
|The four vertex theorem||p. 62|
|Surfaces in three dimensions|
|What is a surface?||p. 67|
|Smooth surfaces||p. 76|
|Smooth maps||p. 82|
|Tangents and derivatives||p. 85|
|Normals and orientability||p. 89|
|Examples of surfaces|
|Level surfaces||p. 95|
|Quadric surfaces||p. 97|
|Ruled surfaces and surfaces of revolution||p. 104|
|Compact surfaces||p. 109|
|Triply orthogonal systems||p. 111|
|Applications of the inverse function theorem||p. 116|
|The first fundamental form|
|Lengths of curves on surfaces||p. 121|
|Isometries of surfaces||p. 126|
|Conformal mappings of surfaces||p. 133|
|Equiareal maps mid a theorem of Archimedes||p. 139|
|Spherical geometry||p. 148|
|Curvature of surfaces|
|The second fundamental form||p. 159|
|The Gauss and Weingarten maps||p. 162|
|Normal and geodesic curvatures||p. 165|
|Parallel transport and covariant derivative||p. 170|
|Gaussian, mean and principal curvatures|
|Gaussian and mean curvatures||p. 179|
|Principal curvatures of a surface||p. 187|
|Surfaces of constant Gaussian curvature||p. 196|
|Flat surfaces||p. 201|
|Surfaces of constant mean curvature||p. 206|
|Gaussian curvature of compact surfaces||p. 212|
|Definition and basic properties||p. 215|
|Geodesic equations||p. 220|
|Geodesics on surfaces of revolution||p. 227|
|Geodesics as shortest paths||p. 235|
|Geodesic coordinates||p. 242|
|Gauss' Theorema Egregium|
|The Gauss and Codazzi-Mainardi equations||p. 247|
|Gauss' remarkable theorem||p. 252|
|Surfaces of constant Gaussian curvature||p. 257|
|Geodesic mappings||p. 263|
|Upper half-plane model||p. 270|
|Isometries of H||p. 277|
|Poincaré disc model||p. 283|
|Hyperbolic parallels||p. 290|
|Beltrami-Klein model||p. 295|
|Plateau's problem||p. 305|
|Examples of minimal surfaces||p. 312|
|Gauss map of a minimal surface||p. 320|
|Conformal parametrization of minimal surfaces||p. 322|
|Minimal surfaces and holomorphic functions||p. 325|
|The Gauss-Bonnet theorem|
|Gauss-Bonnet for simple closed curves||p. 335|
|Gauss-Bonnet for curvilinear polygons||p. 342|
|Integration on compact surfaces||p. 346|
|Gauss-Bonnet for compact surfaces||p. 349|
|Map colouring||p. 357|
|Holonomy and Gaussian curvature||p. 362|
|Singularities of vector fields||p. 365|
|Critical points||p. 372|
|Inner product spaces and self-adjoint linear maps|
|Isometries of Euclidean spaces|
|Hints to selected exercises|
|Table of Contents provided by Ingram. All Rights Reserved.|