OurBigBook About$ Donate
 Sign in Sign up

Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics V / 2 / a / ii

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Oxford 2015 Prelims Mathematics V 2 a
2026-10-25  0 By others on same topic  0 Discussions Create my own version
  • Table of contents
    • Solution ii

Solution

 0  0
ii
Apply the product rule to each vector component and sum:
∇⋅(ϕF)​=j=1∑3​∂xj​​(ϕFj​)=ϕj=1∑3​∂xj​​Fj​+j=1∑3​(∂xj​​ϕ)Fj​=ϕ∇⋅F+∇ϕ⋅F.​​
(1)
Thus the divergence of a scalar field times a vector field contains a divergence term and a dot product with the gradient of the scalar field.

 Ancestors (12)

  1. a
  2. 2
  3. Mathematics V
  4. Prelims
  5. 2015
  6. Past exam of the mathematics course of the University of Oxford
  7. Mathematics course of the University of Oxford
  8. Undergraduate course of the University of Oxford
  9. Course of the University of Oxford
  10. University of Oxford
  11. List of universities
  12.  Home

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook