By Siavash Shahshahani

ISBN-10: 0486807061

ISBN-13: 9780486807065

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.

Show description

Read Online or Download An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) PDF

Similar geometry & topology books

D. Wang's Elimination Methods (Texts & Monographs in Symbolic PDF

The advance of polynomial-elimination suggestions from classical idea to trendy algorithms has gone through a tortuous and rugged direction. this is saw L. van der Waerden's removing of the "elimination concept" bankruptcy from from B. his vintage glossy Algebra in later variations, A. Weil's desire to put off "from algebraic geometry the final strains of removal theory," and S.

Vector Analysis Versus Vector Calculus (Universitext) by Antonio Galbis PDF

The purpose of this ebook is to facilitate using Stokes' Theorem in applications.  The textual content takes a differential geometric standpoint and offers for the coed a bridge among natural and utilized arithmetic by means of conscientiously construction a proper rigorous improvement of the subject and following this via to concrete purposes in and 3 variables.

Download e-book for kindle: Algebraic Topology: A First Course (Graduate Texts in by William Fulton

To the instructor. This ebook is designed to introduce a scholar to a couple of the real principles of algebraic topology by means of emphasizing the re­ lations of those rules with different parts of arithmetic. instead of settling on one viewpoint of modem topology (homotopy conception, simplicial complexes, singular conception, axiomatic homology, fluctuate­ ential topology, and so forth.

Read e-book online Geometry and Integrability (London Mathematical Society PDF

So much integrable platforms owe their foundation to difficulties in geometry and they're top understood in a geometric context. this is often very true this day while the heroic days of KdV-type integrability are over. difficulties that may be solved utilizing the inverse scattering transformation have reached the purpose of diminishing returns.

Additional resources for An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals)

Sample text

Download PDF sample

An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) by Siavash Shahshahani

by Mark

Rated 4.74 of 5 – based on 38 votes