Geometry Topology

An Introductory Course on Differentiable Manifolds (Aurora: - download pdf or read online

By Siavash Shahshahani

Based on writer Siavash Shahshahani's broad instructing adventure, this quantity provides a radical, rigorous path at the conception of differentiable manifolds. aimed toward complex undergraduates and graduate scholars in arithmetic, the treatment's necessities contain a powerful historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, straightforward summary algebra, and element set topology. greater than two hundred routines provide scholars considerable chance to gauge their talents 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 spinoff. half III, related to manifolds and vector bundles, develops the most physique of the direction. the ultimate bankruptcy offers 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. correct old and philosophical asides increase 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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