By Siavash Shahshahani
Based on writer Siavash Shahshahani's wide instructing adventure, this quantity offers a radical, rigorous path at the idea of differentiable manifolds. aimed toward complicated undergraduates and graduate scholars in arithmetic, the treatment's must haves contain a robust historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, straight forward summary algebra, and element set topology. greater than two hundred routines provide scholars abundant 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, related to manifolds and vector bundles, develops the most physique of the direction. 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. appropriate ancient and philosophical asides improve the mathematical textual content, and useful Appendixes supply supplementary material.
Read or Download An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) PDF
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