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Contents
Contents
Differential Geometry. Honours 1996
Michael Murray
Contents
Co-ordinate independent calculus.
Introduction
Smooth functions
Derivatives as linear operators.
The chain rule.
Diffeomorphisms and the inverse function theorem.
Differentiable manifolds
Co-ordinate charts
Linear manifolds.
Topology of a manifold
Smooth functions on a manifold.
The tangent space.
The derivative of a function.
Co-ordinate tangent vectors and one-forms.
How to calculate.
Submanifolds
Tangent space to a submanifold
Smooth functions between manifolds
The tangent to a smooth map.
Submanifolds again.
Vector fields.
The Lie bracket.
Differential forms.
The exterior algebra of a vector space.
Differential forms and the exterior derivative.
Pulling back differential forms
Integration of differential forms
Orientation.
Integration again
Stokes theorem.
Manifolds with boundary.
Stokes theorem.
Partitions of unity.
Vector fields and the tangent bundle.
Vector fields and derivations.
Tensor products
About this document ...
Michael Murray
1998-09-16
