![]() ![]() 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. "synopsis" may belong to another edition of this title.Ĭurves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Each book includes numerous examples, problems and fully worked solutions. 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. The Springer Undergraduate Mathematics Series (SUMS) is a series designed for undergraduates in mathematics and the sciences worldwide. ![]() Andrew Pressley is Professor of Mathematics at King’s College London, UK. The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecturers, and for all others interested in the subject. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. 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. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. The only prerequisites are one year of undergraduate calculus and linear algebra.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. ![]() Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss-Bonnet theorem. ![]() Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. The link between the physical world and its visualization is geometry. ![]()
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