Siavash Shahshahani's An Introductory Course on Differentiable Manifolds (Aurora: PDF

By Siavash Shahshahani

Based on writer Siavash Shahshahani's vast educating event, this quantity offers a radical, rigorous path at the idea of differentiable manifolds. aimed at complex undergraduates and graduate scholars in arithmetic, the treatment's necessities comprise a powerful historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, basic summary algebra, and aspect set topology. greater than two hundred routines provide scholars abundant 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 by-product. half III, related to manifolds and vector bundles, develops the most physique of the path. 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 spinoff of vector fields at the base manifold. proper ancient and philosophical asides improve the mathematical textual content, and useful 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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