![]() ![]() ![]() The requisite point-set topology is included in an appendix of twenty pages other appendices review facts from real analysis and linear algebra. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. ![]() The formulation and presentation are largely based on a tensor calculus approach. The book, which consists of 260 pages, is about differential geometry of space curves and surfaces. Around 200 additional exercises, and a full solutions manual for instructors, available via is the balck and white version of the book. Around 200 additional exercises, and a full solutions manual for instructors, available via Description 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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