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J. Munkres, Analysis on Manifolds, Cambridge, MA: Perseus Publishing, 1991. "; $programm = "

Definition and examples of smooth manifolds.

Orientability and orientation.

Tangent vectors and tangent space to a manifold at a point. Tangent bundles. Vector fields.

Skew-symmetric forms on linear spaces. Wedge product.

Differential forms on manifolds. Exterior differential.

Smooth maps of manifolds. Diffeomorphisms. The transformation rule under coordinate change for functions, vector fields and differential forms.

Integration in . Coordinate change in the integral. Integration of differential forms. Stokes theorem for a cube in .

Integration on manifolds.

Manifold with boundary. Induced orientation of the boundary.

General Stokes theorem. Green's formula, Gauss-Ostrogradskii divergence theorem, Stokes formula for a surface in .

Closed and exact forms. The Poincare lemma. De Rham cohomology. "; ?>