An Introductory Course on Differentiable Manifolds (Aurora: by Siavash Shahshahani PDF
By Siavash Shahshahani
Based on writer Siavash Shahshahani's broad instructing adventure, this quantity provides a radical, rigorous direction at the thought of differentiable manifolds. aimed at complex undergraduates and graduate scholars in arithmetic, the treatment's must haves comprise a powerful history in undergraduate arithmetic, together with multivariable calculus, linear algebra, trouble-free summary algebra, and element set topology. greater than two hundred routines supply scholars abundant 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 by-product. half III, regarding manifolds and vector bundles, develops the most physique of the path. the ultimate bankruptcy presents a glimpse into geometric buildings via 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. proper ancient and philosophical asides improve the mathematical textual content, and important 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