By Siavash Shahshahani
Based on writer Siavash Shahshahani's wide educating adventure, this quantity provides an intensive, rigorous path at the idea of differentiable manifolds. aimed toward complex undergraduates and graduate scholars in arithmetic, the treatment's necessities comprise a robust history in undergraduate arithmetic, together with multivariable calculus, linear algebra, easy summary algebra, and aspect set topology. greater than 2 hundred routines supply scholars plentiful chance to gauge their abilities and achieve extra insights.
The four-part remedy 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 by-product, and Lie spinoff. half III, regarding manifolds and vector bundles, develops the most physique of the path. the ultimate bankruptcy presents a glimpse into geometric buildings through 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 old and philosophical asides improve the mathematical textual content, and valuable Appendixes provide supplementary material.
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Additional 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