By Siavash Shahshahani

ISBN-10: 0486807061

ISBN-13: 9780486807065

Based on writer Siavash Shahshahani's huge educating adventure, this quantity provides a radical, rigorous direction at the idea of differentiable manifolds. aimed at complicated undergraduates and graduate scholars in arithmetic, the treatment's necessities comprise a robust heritage in undergraduate arithmetic, together with multivariable calculus, linear algebra, trouble-free summary algebra, and element set topology. greater than 2 hundred routines supply scholars considerable chance to gauge their talents and achieve extra insights.
The four-part remedy starts with a unmarried bankruptcy dedicated to the tensor algebra of linear areas and their mappings. half II brings in neighboring issues to discover integrating vector fields, Lie bracket, external spinoff, and Lie by-product. half III, concerning manifolds and vector bundles, develops the most physique of the path. the ultimate bankruptcy offers a glimpse into geometric constructions via introducing connections on the tangent package as a device to implant the second one spinoff and the by-product of vector fields at the base manifold. correct historic and philosophical asides increase the mathematical textual content, and invaluable Appendixes provide supplementary material.

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An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) by Siavash Shahshahani

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