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Calculus III - Conceptual Help

  1. Apr 28, 2014 #1
    I'm taking a Calc III Course and I want to know if anyone out there can help me with a few conceptual ideas. I know how to do the math but I am missing the conceptual idea of it.

    Why should/do we we parametrize?
    Why should/do we convert to Polar or Cylindrical?


    These basic ideas should be easy enough for me at this point but for some reason I keep mixing things up. I tried to searching the web and other sources but I keep finding information on the actual process, and they all pass the big idea I am looking for. Idk maybe I'm not the best at searching these things...

    Thanks in advance. I really appreciate it
     
  2. jcsd
  3. Apr 28, 2014 #2

    SteamKing

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    We do these things (parameterization, changing coordinate systems) to make analyzing a problem easier.

    To take a simple example, we can calculate the area of a circle using cartesian coordinates and some sophisticated integration and come up with A = πr[itex]^{2}[/itex]. By changing the problem to polar coordinates,

    A = [itex]\int[/itex][itex]^{2π}_{0}[/itex] r[itex]^{2}[/itex]/2 dθ,

    where r = radius of the circle = constant, which is much easier to evaluate than

    A = 2*[itex]\int[/itex][itex]^{r}_{-r}[/itex] (r[itex]^{2}[/itex]-x[itex]^{2}[/itex])[itex]^{1/2}[/itex] dx
     
  4. Apr 28, 2014 #3
    Understood, I need more practice.

    I want to be able to quickly identify which coordinate system to convert to when given a problem. It doesn't seem like there is any sort of general case because problems can be done in multiple ways. Am I accurate with that assumption?
     
  5. Apr 29, 2014 #4

    SteamKing

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    Yes, you are. This is why some things about studying math and science only come with the experience of working out a variety of problems.
     
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