Honors Calculus 252-2

Review Sheet for Final

Note: As always for review sheets: do only the problems you have difficulties with.

1. 8.1.3, 8.1.10, 8.1.8v+vi,

2. Determine the streamlines for the flow given by
   

   v = ( -y x2+y2 , x x2+y2 ,0). (1)

3. 8.2.1, then redo 8.2.1 with the vector field F = (2x+3y,3x-2y,0). Compare the two cases. Do you see a qualitative difference?

4. 8.2.12

5. For the magnetic field B = (y,z,x) determine a vector potential A such that B = Ñ×A.

6. Consider the vector field v = (x,y+az,z+by).

   1. For which values of a and b is v conservative?
   2. Under which condition can v be written as v = Ñf? Determine f for the cases for which it is possible.
   3. For a = 1 and b = 1 determine
      

      ó õ C  v·dr (2)

      where the contour C is given by
      

      r(t) = (2t, 8t 2+t , 4t   ___ Ö2+t )       with       0 £ t £ 2. (3)

7. 8.3.4, 8.3.12, 8.3.14

8. 8.4.4, 8.4.14, 8.4.18

9. 8.5.1, 8.5.10

10. For the flow field v = (x²,xy,yz) calculate the net flux across the surface of the cube defined by the corners (0,0,0), (1,0,0), (0,1,0), (0,0,1).

11. 8.6.1, 8.6.13, 8.6.16

12. 7.1.10, 7.1.20

13. 7.2.5, 7.2.24

14. 7.3.13

15. 7.4.7, 7.4.14

16. 7.5.3, 7.5.4