Gradient, divergence and curl

Are you studying for a mathematics degree and in your sophomore year at university? If so this is the ideal quiz for you. It tests the basic principles of vector calculus.

Do you want to be an astrophysicist, a cosmologist or a research mathematician? If so this quiz gives you the basic foundations of your sphere of interest. I have composed each question in such a way that there is no complicated working out but the level tested is respectful in being very advanced.

Created by: John Carpenter

  1. Given that f(x,y,z) = sin(xyz) what is del f ?
  2. Given that f(x,y,z) = xyz + xy + z what is del f ?
  3. What is the divergence of the vector field F where F = xi + yj + zk ?
  4. What is the divergence of the vector field F where F = xzi + yzj + xyk ?
  5. What is the divergence of the vector field F where F = sin xi + sin yj + sin zk ?
  6. What is the divergence of the vector field F where F = xyi + zk ?
  7. What is the divergence of the vector field F where F = xyzi + xyzj + xyzk ?
  8. What is the curl of the vector field F where F = xi + yzj ?
  9. What is the curl of the vector field F where F = yzi + xyj + xzk ?
  10. What is the curl of the vector field F where F = xi + xyzj + zk ?

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