Read e-book online An Introductory Course on Differentiable Manifolds (Aurora: PDF

By Siavash Shahshahani

Based on writer Siavash Shahshahani's wide educating adventure, this quantity provides an intensive, rigorous path at the concept of differentiable manifolds. aimed toward complex undergraduates and graduate scholars in arithmetic, the treatment's must haves contain a robust historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, user-friendly summary algebra, and element set topology. greater than 2 hundred routines provide scholars plentiful chance to gauge their abilities and achieve extra insights.
The four-part remedy starts off 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, related to manifolds and vector bundles, develops the most physique of the path. the ultimate bankruptcy offers a glimpse into geometric buildings by way of introducing connections on the tangent package as a device to implant the second one by-product and the by-product of vector fields at the base manifold. proper historic and philosophical asides improve the mathematical textual content, and worthy 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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