Differential Geometry. Honours 1996
Co-ordinate independent calculus.
Derivatives as linear operators.
The chain rule.
Diffeomorphisms and the inverse function theorem.
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.
Tangent space to a submanifold
Smooth functions between manifolds
The tangent to a smooth map.
The Lie bracket.
The exterior algebra of a vector space.
Differential forms and the exterior derivative.
Pulling back differential forms
Integration of differential forms
Manifolds with boundary.
Partitions of unity.
Vector fields and the tangent bundle.
Vector fields and derivations.
About this document ...