By Siavash Shahshahani
Based on writer Siavash Shahshahani's broad instructing adventure, this quantity provides an intensive, rigorous direction at the concept of differentiable manifolds. aimed toward complex undergraduates and graduate scholars in arithmetic, the treatment's necessities contain a robust historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, hassle-free summary algebra, and aspect set topology. greater than two hundred routines supply scholars plentiful chance to gauge their talents 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, concerning manifolds and vector bundles, develops the most physique of the direction. the ultimate bankruptcy offers a glimpse into geometric constructions via 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 old and philosophical asides improve the mathematical textual content, and valuable Appendixes supply supplementary material.
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Extra info for An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals)
An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) by Siavash Shahshahani