Based on writer Siavash Shahshahani's huge educating event, this quantity offers an intensive, rigorous direction at the thought of differentiable manifolds. aimed toward complicated undergraduates and graduate scholars in arithmetic, the treatment's must haves comprise a powerful heritage in undergraduate arithmetic, together with multivariable calculus, linear algebra, user-friendly summary algebra, and aspect set topology. greater than 2 hundred workouts supply scholars abundant chance to gauge their talents and achieve extra insights.
The four-part therapy 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, concerning 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 deal as a device to implant the second one spinoff and the by-product of vector fields at the base manifold. proper old and philosophical asides increase the mathematical textual content, and important Appendixes supply supplementary material.
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