17. Divergence, Curl and Potentials - Contents

1. The Del Operator

     1
   1. The Del Operator

2. The Divergence Operator

     1   2
   1. Algebraic Definition of Divergence
   2. Geometric Interpretation of the Divergence

3. The Curl Operator

     1   2
   1. Algebraic Definition of Curl
   2. Geometric Interpretation of the Curl

4. Differential Identities

     1   2
   1. First Order Differential Identities
   2. Second Order Differential Operators and Identities
      1. The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian
      2. The Curl of a Gradient (\(\vec\nabla\times\vec\nabla f\))
      3. The Divergence of a Curl (\(\vec\nabla\cdot\vec\nabla\times\vec F\))
      4. The Curl of a Curl (\(\vec\nabla\times\vec\nabla\times\vec F\))

5. Generalizing Antiderivatives

     1
   1. Generalizing Antiderivatives

6. Scalar Potentials

     1   2
   1. Finding Scalar Potentials
   2. Non-Existence of a Scalar Potential

7. Vector Potentials

     1   2
   1. Finding Vector Potentials
   2. Non-Existence of a Vector Potential

8. Exercises

     1
   1. Exercises