Math crossword 3rd round

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Across
  1. 3. Measure of outward flux density of a vector field
  2. 4. Vector operator representing rotation of a vector field.
  3. 6. Relationship that states two expressions are equal.
  4. 7. Line touching a curve at a point without cutting it nearby.
  5. 9. A rule used to solve mathematical problems.
  6. 12. Series expansion of a function about a point.
  7. 13. Scalar associated with a matrix transformation
  8. 14. Sum of diagonal elements of a square matrix.
  9. 15. Square matrix with ones on the diagonal and zeros elsewhere.
  10. 17. Dimension of column space of a matrix
  11. 18. Scalar value indicating how much a matrix scales area or volume.
  12. 19. Vectors whose dot product equals zero.
Down
  1. 1. Rate of change of a function with respect to a variable.
  2. 2. Matrix obtained by interchanging rows and columns.
  3. 5. Graph of a quadratic function.
  4. 8. Value where a function approaches but may notreach.
  5. 10. Direction of steepest increase of a scalar field
  6. 11. Inverse operation of differentiation
  7. 16. Solution of a differential equation containing arbitrary constants.