Name:
I.D.:
Physics 50 2012 Final
1. (3 pts) Express sin x in terms of exp(ix) and exp(ix). Show work.
2. (4 pts) The table compares three types of vector spaces. Complete
the two missing entries: (a) the basis in the vector row and (b) the
spectrum in th
Name:
Physics 50 2013 Final
1. (5 pts) The coordinate transformation equations between Cartesian
(x, y, z ) coordinates and parabolic cylinder (u, v, z ) coordinates are
12
(u v 2 )
x=
2
y = uv
z=z
The scale factors for this transformation (which you need