RE: Math 293 Prelim 3, and some old exams. 11/15/96
1) You should be able to draw neat sketches from which
you can reasonably find the following equations related to area, line, and
volume integrals. Thus you need not memorize these formulas for the
prelim (though you will probably remember them if you are good at
deriving them).
dA = dx dy
= r dr d theta
dV = dx dy dz
= r dr d(theta) dz
= rho^2 sin(phi) d(rho d(phi) d(theta)
x = r cos(theta)
= rho sin(phi) cos(theta)
y = r sin(theta)
= rho sin(phi) sin(theta)
z = rho cos(phi)
ds = sqrt( (dx)^2 + (dy)^2 ) = vel dt
unit tangent = T = vel / vel

as well as other variants needed, for example, to work out the
equivalance of the formulas of page 1070 of the text.
2) A group of students and faculty are assembling old exams for the
courses 191,193, 192, 292, 294. This is an ongoing project. It just
went public this week. The link to these old exams (old 294 is most
relevant to this class) can be found on the course WWW page under the
section on old 293,294 and old exams.