By Siavash Shahshahani
Based on writer Siavash Shahshahani's wide instructing adventure, this quantity provides a radical, rigorous path at the conception of differentiable manifolds. aimed at complicated undergraduates and graduate scholars in arithmetic, the treatment's necessities contain a robust heritage in undergraduate arithmetic, together with multivariable calculus, linear algebra, effortless summary algebra, and aspect set topology. greater than 2 hundred routines provide scholars considerable chance to gauge their abilities and achieve extra insights.
The four-part remedy 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 spinoff. half III, concerning 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 deal as a device to implant the second one by-product and the spinoff of vector fields at the base manifold. appropriate historic and philosophical asides increase the mathematical textual content, and invaluable 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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