Table of contents for From calculus to cohomology : de Rham cohomology and characteristic classes / Ib Madsen and Jrgen Tornehave.

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1. Introduction
2. The alternating algebra
3. De Rham cohomology
4. Chain complexes and their cohomology
5. The Mayer-Vietoris sequence
6. Homotopy
7. Applications of De Rham cohomology
8. Smooth manifolds
9. Differential forms on smooth manifolds
10. Integration on manifolds
11. Degree, linking numbers and index of vector fields
12. The Poincare;-Hopf theorem
13. Poincare
duality
14. The complex projective space CPn
15. Fiber bundles and vector bundles
16. Operations on vector bundles and their sections
17. Connections and curvature
18. Characteristic classes of complex vector bundles
19. The Euler class
20. Cohomology of projective and Grassmanian bundles
21. Thom isomorphism and the general Gauss-Bonnet formula.