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List of corrections The following gives a list of corrections to the textbook “From Calculus to Cohomology. De Rham cohomology and characteristic classes” by I. Madsen and J. Tornehave. If there is a minus in front of the line number one has to count from the bottom. • p. 1 l.16 In the first line of Example 1.2, change f : R2 → R2 to f : R2 − {0} → R2 . • p. 4 l.9 In the formula for rot(f1 , f2 , f3 ) the last entry should be changed from ∂f2 ∂f1 to ∂x − ∂x . 1 2 ∂f1 ∂f2 − ∂x ∂x2 2 • p. 8 l.5 Change (ω1 ∧ ω2 ) = to (ω1 ∧ ω2 )(ξ1 , ξ2 ) =. • p. 13 l.13 Change Theorem 2.18 to Theorem 2.16. • p. 13 l.19 and l.-2 Change det(f − t) to det(f − tid) or det(f − tidV ). • p. 16 l.-7 There should be d’s above the mapping arrows in Ωp (U ) → Ωp+1 (U ) → Ωp+2 (U ). • p. 17 l.-10 Change “an anti-commutative algebra Ω∗ (U )” to “an anti-commutative graded algebra Ω∗ (U )”. • p. 30 l.-4 Change “(Long exact homology sequence)” to “(Long exact cohomology sequence)”. • p. 36 l.-11 Change H p (R − {0}) to H p (R2 − {0}). • p. 243 l.2 In Exercise 1.1, change “of Theorem 1.7.” to “of Example 1.7.” • p. 243 l.6 Change “in Example 1.8” to “in Example 1.7”. • p. 243 l.-4 Change “where {b∗1 , . . . , b∗k } is” to “where {b∗1 , . . . , b∗n } is”. • p. 245 l.15 Change “with vol(1 , . . . , n ) = 1” to “with vol(e1 , . . . , en ) = 1”. 1