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Chapter 19 The Exterior Derivative

This chapter explores the exterior derivative on a coordinate chart, local operators, extension of local forms to global forms, existence and uniqueness of exterior differentiation, restriction of k-forms to submanifolds, nowhere-vanishing 1-forms on a circle, and exterior differentiation under pullback. It also provides problem solutions.

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Chapter 19 The Exterior Derivative

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  1. Chapter 19The Exterior Derivative • Contents: • Exterior Derivative on a Coordinate Chart • Local Operators • Extension of a Local Form to a Global Form • Existence of an Exterior Differentiation • Uniqueness of Exterior Differentiation • The Restriction of a k-Form to a Submanifold • A Nowhere-Vanishing 1-Form on the Circle • Exterior Differentiation Under a Pullback • Problems

  2. 19.1 Exterior Derivative on a Coordinate Chart

  3. 19.2 Local Operators

  4. 19.3 Extension of a Local Form to a Global Form

  5. 19.4 Existence of an Exterior Differentiation

  6. 19.5 Uniqueness of Exterior Differentiation

  7. 19.6 The Restriction of a k-Form to a Submanifold

  8. 19.7 A Nowhere-Vanishing 1-Form on the Circle

  9. 19.8 Exterior Differentiation Under a Pullback

  10. Problems Solution:

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