![]() ![]() This new introduction to differential geometry makes use of Javaapplets instead of software to help readers to generate pictures. Hints for most of the 124 exercises appear at the back ofthe book.īanchoff, Thomas and Lovett, Stephen, Differential Geometry ofCurves and Surfaces, A K Peters, 2010, hardcover, xvi + 331 pp.,ISBN 9781568814568. ![]() Along the way, theauthor discusses the exponential map, parallel transport, Jacobifields, minimal surfaces, spherical and hyperbolic geometry,cartography, Gauss’ divergence theorem, and the Gauss-Bonnettheorem. The book starts with a chapter onEuclidean geometry, then studies the local and global geometry ofcurves and surfaces in three-dimensional space. I find this to be a rather sophisticated introduction to thedifferential geometry of curves and surfaces, though the author says thathe avoids the formalism necessary for a deeper study of differentialgeometry as much as possible. It contains lots of helpful illustrations, examples, and exercises.īär, Christian, Elementary Differential Geometry,Cambridge University Press, 2010, xii + 317 pp. The goal of this little book is to make the topic of differentialforms accessible to students at the sophomore level and above. "Excellent figures supplement a good account, sprinkled with illustrative examples.Differential Geometry References Annotated List of Books and Websites on ElementaryDifferential Geometryĭaniel Drucker, Wayne State University (last updated August 28, 2010) Bachman, David, A Geometric Approach to DifferentialForms, Birkhauser, 2006, hardcover, 140 pp., ISBN 0817644997. "The text is nicely illustrated, the definitions are well-motivated and the proofs are particularly well-written and student-friendly.this book would make an excellent text for an undergraduate course, but could also well be used for a reading course, or simply read for pleasure." Around 200 additional exercises, and a full solutions manual for instructors, available via Praise for the first edition:. ![]() Coverage of topics such as: parallel transport and its applications map colouring holonomy and Gaussian curvature.The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments.New features of this revised and expanded second edition include: 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. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.Įlementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Differential geometry is concerned with the precise mathematical formulation of some of these questions. Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. ![]()
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