Vector calculus

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Across
  1. 2. Matrix of all first-order partial derivatives
  2. 6. Line integral of a vector field around a closed loop
  3. 7. Theorem relating surface integrals to line integrals
  4. 8. Generalization of scalars, vectors, and matrices
  5. 11. Quantity with both magnitude and direction
  6. 12. Scalar product of two vectors
  7. 13. Sum of second partial derivatives
  8. 15. Vector perpendicular to a surface
  9. 16. Operator used for gradient, divergence, and curl
  10. 18. Flow of a vector field through a surface
  11. 19. Vector product perpendicular to two vectors
Down
  1. 1. Directional change of a scalar field
  2. 3. Field with zero curl; path-independent work
  3. 4. A function assigning vectors or scalars to points
  4. 5. Quantity with magnitude only, no direction
  5. 9. Field with zero curl everywhere
  6. 10. Scalar function whose gradient gives a vector field
  7. 14. Rotation or circulation of a vector field
  8. 16. Outflow of a vector field at a point
  9. 17. Theorem relating divergence to flux through a surface