Based on writer Siavash Shahshahani's wide instructing adventure, this quantity offers a radical, rigorous direction at the idea of differentiable manifolds. aimed toward complicated undergraduates and graduate scholars in arithmetic, the treatment's must haves comprise a powerful historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, hassle-free summary algebra, and element set topology. greater than 2 hundred routines supply scholars plentiful chance to gauge their abilities and achieve extra insights.
The four-part therapy 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 spinoff. half III, related to manifolds and vector bundles, develops the most physique of the direction. the ultimate bankruptcy presents a glimpse into geometric constructions through 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. appropriate old and philosophical asides increase the mathematical textual content, and useful Appendixes provide supplementary material.
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