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Appendix D List of exercises

1 A preview of vector calculus

2 One-forms and vector fields

Exercise 2.1.3.1
Exercise 2.1.3.2
Exercise 2.1.3.3
Exercise 2.1.3.4
Exercise 2.2.5.1
Exercise 2.2.5.2
Exercise 2.2.5.3
Exercise 2.2.5.4
Exercise 2.2.5.5
Exercise 2.2.5.6
Exercise 2.2.5.7
Exercise 2.2.5.8
Exercise 2.2.5.9
Exercise 2.3.3.1
Exercise 2.3.3.2
Exercise 2.3.3.3
Exercise 2.4.3.1
Exercise 2.4.3.2
Exercise 2.4.3.3
Exercise 2.4.3.4
Exercise 2.4.3.5
Exercise 2.4.3.6

3 Integrating one-forms: line integrals

Exercise 3.1.5.1
Exercise 3.1.5.2
Exercise 3.1.5.3
Exercise 3.2.6.1
Exercise 3.2.6.2
Exercise 3.2.6.3
Exercise 3.2.6.4
Exercise 3.2.6.5
Exercise 3.2.6.6
Exercise 3.3.5.1
Exercise 3.3.5.2
Exercise 3.3.5.3
Exercise 3.3.5.4
Exercise 3.3.5.5
Exercise 3.4.3.1
Exercise 3.4.3.2
Exercise 3.4.3.3
Exercise 3.4.3.4
Exercise 3.4.3.5
Exercise 3.5.3.1
Exercise 3.5.3.2
Exercise 3.5.3.3
Exercise 3.6.3.1
Exercise 3.6.3.2
Exercise 3.6.3.3
Exercise 3.6.3.4

4 \(k\)-forms

Exercise 4.1.5.1
Exercise 4.1.5.2
Exercise 4.1.5.3
Exercise 4.1.5.4
Exercise 4.1.5.5
Exercise 4.2.3.1
Exercise 4.2.3.2
Exercise 4.2.3.3
Exercise 4.2.3.4
Exercise 4.2.3.5
Exercise 4.2.3.6
Exercise 4.3.4.1
Exercise 4.3.4.2
Exercise 4.3.4.3
Exercise 4.3.4.4
Exercise 4.3.4.5
Exercise 4.3.4.6
Exercise 4.3.4.7
Exercise 4.3.4.8
Exercise 4.3.4.9
Exercise 4.4.5.1
Exercise 4.4.5.2
Exercise 4.4.5.3
Exercise 4.4.5.4
Exercise 4.4.5.5
Exercise 4.4.5.6
Exercise 4.4.5.7
Exercise 4.5.4.1
Exercise 4.5.4.2
Exercise 4.5.4.3
Exercise 4.5.4.4
Exercise 4.5.4.5
Exercise 4.5.4.6
Exercise 4.6.3.1
Exercise 4.6.3.2
Exercise 4.6.3.3
Exercise 4.6.3.4
Exercise 4.6.3.5
Exercise 4.6.3.6
Exercise 4.7.5.1
Exercise 4.7.5.2
Exercise 4.7.5.3
Exercise 4.7.5.4
Exercise 4.7.5.5
Exercise 4.7.5.6
Exercise 4.7.5.7
Exercise 4.8.4.1
Exercise 4.8.4.2
Exercise 4.8.4.3
Exercise 4.8.4.4
Exercise 4.8.4.5
Exercise 4.8.4.6

5 Integrating two-forms: surface integrals

Exercise 5.1.4.1
Exercise 5.1.4.2
Exercise 5.1.4.3
Exercise 5.1.4.4
Exercise 5.1.4.5
Exercise 5.1.4.6
Exercise 5.2.3.1
Exercise 5.2.3.2
Exercise 5.2.3.3
Exercise 5.2.3.4
Exercise 5.2.3.5
Exercise 5.3.3.1
Exercise 5.3.3.2
Exercise 5.3.3.3
Exercise 5.3.3.4
Exercise 5.3.3.5
Exercise 5.4.4.1
Exercise 5.4.4.2
Exercise 5.4.4.3
Exercise 5.4.4.4
Exercise 5.5.4.1
Exercise 5.5.4.2
Exercise 5.5.4.3
Exercise 5.5.4.4
Exercise 5.6.4.1
Exercise 5.6.4.2
Exercise 5.6.4.3
Exercise 5.6.4.4
Exercise 5.6.4.5
Exercise 5.7.3.1
Exercise 5.7.3.2
Exercise 5.7.3.3
Exercise 5.7.3.4
Exercise 5.7.3.5
Exercise 5.8.3.1
Exercise 5.8.3.2
Exercise 5.8.3.3
Exercise 5.8.3.4
Exercise 5.8.3.5
Exercise 5.8.3.6
Exercise 5.9.3.1
Exercise 5.9.3.2
Exercise 5.9.3.3
Exercise 5.9.3.4

6 Beyond one- and two-forms

Exercise 6.2.3.1
Exercise 6.2.3.2
Exercise 6.2.3.3
Exercise 6.2.3.4
Exercise 6.2.3.5
Exercise 6.4.3.1
Exercise 6.4.3.2

7 Unoriented line and surface integrals

Exercise 7.1.3.1
Exercise 7.1.3.2
Exercise 7.1.3.3
Exercise 7.1.3.4
Exercise 7.1.3.5
Exercise 7.2.3.1
Exercise 7.2.3.2
Exercise 7.2.3.3
Exercise 7.2.3.4
Exercise 7.2.3.5
Exercise 7.3.3.1
Exercise 7.3.3.2
Exercise 7.3.3.3