By Siavash Shahshahani
Based on writer Siavash Shahshahani's wide instructing event, this quantity provides a radical, rigorous direction at the concept of differentiable manifolds. aimed at complex undergraduates and graduate scholars in arithmetic, the treatment's must haves contain a powerful heritage in undergraduate arithmetic, together with multivariable calculus, linear algebra, common summary algebra, and element set topology. greater than 2 hundred workouts supply scholars plentiful chance to gauge their talents 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 spinoff, and Lie spinoff. half III, regarding manifolds and vector bundles, develops the most physique of the direction. the ultimate bankruptcy offers a glimpse into geometric constructions by means of introducing connections on the tangent package as a device to implant the second one by-product and the spinoff of vector fields at the base manifold. suitable old and philosophical asides improve the mathematical textual content, and worthy Appendixes supply 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