By Siavash Shahshahani
Based on writer Siavash Shahshahani's wide instructing adventure, this quantity provides an intensive, rigorous direction at the conception of differentiable manifolds. aimed at complicated undergraduates and graduate scholars in arithmetic, the treatment's must haves comprise a powerful heritage in undergraduate arithmetic, together with multivariable calculus, linear algebra, simple summary algebra, and aspect set topology. greater than 2 hundred routines provide scholars plentiful chance to gauge their abilities and achieve extra insights.
The four-part therapy 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, related to manifolds and vector bundles, develops the most physique of the direction. the ultimate bankruptcy presents a glimpse into geometric constructions via introducing connections on the tangent package as a device to implant the second one spinoff and the spinoff of vector fields at the base manifold. suitable ancient and philosophical asides improve the mathematical textual content, and necessary Appendixes provide supplementary material.
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Extra resources 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