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