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Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum nothing beyond first courses in linear algebra and multivariable calculus and the most direct and straightforward approach is used throughout.
New features of this revised and expanded second edition include:
a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.
Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com
List of contents
Curves in the plane and in space.- How much does a curve curve?.- Global properties of curves.- Surfaces in three dimensions.- Examples of surfaces.- The first fundamental form.- Curvature of surfaces.- Gaussian, mean and principal curvatures.- Geodesics.- Gauss Theorema Egregium.- Hyperbolic geometry.- Minimal surfaces.- The Gauss Bonnet theorem.
About the author
Andrew Pressley is Professor of Mathematics at King’s College London, UK.
Summary
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject.
Additional text
. Gouvêa, The Mathematical Association of America, May, 2010)
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From the reviews of the second edition:
Pressley s gives you a very comprehensible and down to earth introduction to differential geometry. the book contains lots of examples and fully worked answers to all exercises, which makes it perfect for self-study. This book will also appeal to those who want to learn on their own, as every problem has a hint/solution in the back. If you want a very general introduction of Differential Geometry, this is the book to start. (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013)
I am very happy to report that the new edition of Pressley s Elementary Differential Geometry is an even better book than the first edition . full solutions to all problems given in an appendix. Most of the problems are in the book and have solutions in the back. The upshot is that this is still an excellent book and still my first choice for an undergraduate introduction to differential geometry. (Fernando Q. Gouva, The Mathematical Association of America, May, 2010)
