Get An Introductory Course on Differentiable Manifolds (Aurora: PDF

By Siavash Shahshahani

Based on writer Siavash Shahshahani's large instructing event, this quantity offers a radical, rigorous path at the conception of differentiable manifolds. aimed toward complicated undergraduates and graduate scholars in arithmetic, the treatment's must haves comprise a robust historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, user-friendly summary algebra, and element set topology. greater than 2 hundred workouts 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 by-product, and Lie by-product. 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 by-product of vector fields at the base manifold. appropriate ancient and philosophical asides improve the mathematical textual content, and important 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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