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A Course in Differential Geometry and Lie Groups (Paperback)
Loot Price: R1,428
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A Course in Differential Geometry and Lie Groups (Paperback)
Series: Texts and Readings in Mathematics, 22
Expected to ship within 12 - 17 working days
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This book arose out of courses taught by the author. It covers the
traditional topics of differential manifolds, tensor fields, Lie
groups, integration on manifolds and basic differential and
Riemannian geometry. The author emphasizes geometric concepts,
giving the reader a working knowledge of the topic. Motivations are
given, exercises are included, and illuminating nontrivial examples
are discussed. Important features include the following: Geometric
and conceptual treatment of differential calculus with a wealth of
nontrivial examples. A thorough discussion of the much-used result
on the existence, uniqueness, and smooth dependence of solutions of
ODEs. Careful introduction of the concept of tangent spaces to a
manifold. Early and simultaneous treatment of Lie groups and
related concepts. A motivated and highly geometric proof of the
Frobenius theorem. A constant reconciliation with the classical
treatment and the modern approach. Simple proofs of the hairy-ball
theorem and Brouwer's fixed point theorem. Construction of
manifolds of constant curvature a la Chern. This text would be
suitable for use as a graduate-level introduction to basic
differential and Riemannian geometry.
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