Download An Introductory Course on Differentiable Manifolds (Aurora: by Siavash Shahshahani PDF

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.

Show description

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

Similar geometry & topology books

Compactification of Symmetric Spaces (Progress in Mathematics)

The idea that of symmetric house is of imperative significance in lots of branches of arithmetic. Compactifications of those areas were studied from the issues of view of illustration concept, geometry, and random walks. This paintings is dedicated to the examine of the interrelationships between those quite a few compactifications and, specifically, makes a speciality of the martin compactifications.

Handbook of Algebraic Topology

Algebraic topology (also often called homotopy thought) is a flourishing department of recent arithmetic. it's very a lot a world topic and this is often mirrored within the heritage of the 36 top specialists who've contributed to the guide. Written for the reader who already has a grounding within the topic, the quantity involves 27 expository surveys protecting the main lively components of analysis.

The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts)

This article on research of Riemannian manifolds is a radical advent to subject matters coated in complicated study monographs on Atiyah-Singer index conception. the most subject is the research of warmth stream linked to the Laplacians on differential varieties. this gives a unified remedy of Hodge conception and the supersymmetric facts of the Chern-Gauss-Bonnet theorem.

Modules over Operads and Functors (Lecture Notes in Mathematics)

This monograph offers a assessment of the foundation of operad conception. It additionally experiences constructions of modules over operads as a brand new machine to version functors among different types of algebras as successfully as operads version different types of algebras.

Extra info for An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals)

Example text

Download PDF sample

Rated 4.80 of 5 – based on 40 votes