Geometry Topology

Download e-book for iPad: An Introductory Course on Differentiable Manifolds (Aurora: by Siavash Shahshahani

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By Siavash Shahshahani

Based on writer Siavash Shahshahani's broad instructing adventure, this quantity provides a radical, rigorous path at the idea of differentiable manifolds. aimed toward complex undergraduates and graduate scholars in arithmetic, the treatment's must haves comprise a robust history in undergraduate arithmetic, together with multivariable calculus, linear algebra, basic summary algebra, and aspect set topology. greater than two hundred workouts supply scholars plentiful 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 by-product, and Lie by-product. half III, regarding manifolds and vector bundles, develops the most physique of the direction. the ultimate bankruptcy presents a glimpse into geometric constructions by way of introducing connections on the tangent package deal as a device to implant the second one spinoff and the by-product of vector fields at the base manifold. proper old and philosophical asides increase the mathematical textual content, and beneficial Appendixes supply supplementary material.

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


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