1. Chapter 19 The Exterior Derivative Contents: 1. Exterior Derivative on a Coordinate ChartExterior Derivative on a Coordinate Chart 2. Local OperatorsLocal Operators 3. Extension of a Local Form to a Global FormExtension of a Local Form to a Global Form 4. Existence of an Exterior DifferentiationExistence of an Exterior Differentiation 5. Uniqueness of Exterior DifferentiationUniqueness of Exterior Differentiation 6. The Restriction of a k-Form to a SubmanifoldThe Restriction of a k-Form to a Submanifold 7. A Nowhere-Vanishing 1-Form on the CircleA Nowhere-Vanishing 1-Form on the Circle 8. Exterior Differentiation Under a PullbackExterior Differentiation Under a Pullback Problems

4. 19.1 Exterior Derivative on a Coordinate Chart

6. 19.2 Local Operators

9. 19.3 Extension of a Local Form to a Global Form

10. 19.4 Existence of an Exterior Differentiation

12. 19.5 Uniqueness of Exterior Differentiation

14. 19.6 The Restriction of a k-Form to a Submanifold

16. 19.7 A Nowhere-Vanishing 1- Form on the Circle

20. 19.8 Exterior Differentiation Under a Pullback

25. Problems Solution:

27. Hint: