Name: Anonymous 2009-03-20 6:08
It's currently 2:45 and I started at about 12:00, we're covering parametrization of surfaces. Half of the questions we simply applications of formula, but the other half were a bit more complicated. In order to use the formula you first had to parametrize a some surface. Obviously there were easy ones like spheres and ellipsoids but the harder ones consisted of surfaces within surfaces, such as a plane inside of a cylinder or a paraboloid inside a cylinder.
When solving these problems it seemed to me like I was just hoping for a coincidence to occur. Such as I had to parametrize the part of the plane inside a cylinder, which forms an ellipse. I then was able to use the parametrization of an ellipse to get the answer. Similarly, I had to find the surface area of the part of the paraboloid of the form x= f(y,x) inside the cylinder z^2 + y^2 = C, obviously the fact that both the paraboloid and cylinder revolved about the x-axis made the problem much easier, probably easier than the plane-cylinder problem since all I had to for this one was copy the parametrization of a paraboloid and restrict the domain of the parameters.
All in all it was the type of assignment I hate. There are hundreds of potential ways two simple surfaces an intersect and there's really no way to study for them for an exam, so studying is essentially useless. Also, even if you study of hours if you don't get the "trick" behind these questions there really is no way of solving these in time. So basically the problem is that these question rely too heavily on the geometry behind the equations instead of manipulating the equations themselves. It reminds me of my Multivariate Calculus class where I left a question blank on the final: find the area or surface area of the intersection of two cylinders. I answered every other question and I had a good 45 minutes to answer that one but I couldn't for the life of me figure out the trick behind it. After the final I heard two classmates talking about and one told the other that she just memorized the procedure. That's not what math is about, computers can do that, math should be about proofs and derivations, not who can memorize the most.
But the worst part about this assignment is that my roommate has been SNEEZING THIS WHOLE TIME AND ITS DRIVING ME INSANE
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When solving these problems it seemed to me like I was just hoping for a coincidence to occur. Such as I had to parametrize the part of the plane inside a cylinder, which forms an ellipse. I then was able to use the parametrization of an ellipse to get the answer. Similarly, I had to find the surface area of the part of the paraboloid of the form x= f(y,x) inside the cylinder z^2 + y^2 = C, obviously the fact that both the paraboloid and cylinder revolved about the x-axis made the problem much easier, probably easier than the plane-cylinder problem since all I had to for this one was copy the parametrization of a paraboloid and restrict the domain of the parameters.
All in all it was the type of assignment I hate. There are hundreds of potential ways two simple surfaces an intersect and there's really no way to study for them for an exam, so studying is essentially useless. Also, even if you study of hours if you don't get the "trick" behind these questions there really is no way of solving these in time. So basically the problem is that these question rely too heavily on the geometry behind the equations instead of manipulating the equations themselves. It reminds me of my Multivariate Calculus class where I left a question blank on the final: find the area or surface area of the intersection of two cylinders. I answered every other question and I had a good 45 minutes to answer that one but I couldn't for the life of me figure out the trick behind it. After the final I heard two classmates talking about and one told the other that she just memorized the procedure. That's not what math is about, computers can do that, math should be about proofs and derivations, not who can memorize the most.
But the worst part about this assignment is that my roommate has been SNEEZING THIS WHOLE TIME AND ITS DRIVING ME INSANE
FFFFFFFFFFFFFFFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU