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Polar coordinates: advanced set 1

I do not believe this is subject is polar coordinates.

Note by Taylor Lau
3 years, 3 months ago

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Polar coordinates is a way for you to change your perspective of the cartesian plane, to make it easier to understand sometimes complicated functions. There are functions whose cartesian equations are mysterious / hard to work with, but by converting into another frame of reference, gives us a lot more flexibility.

One of the big uses of polar coordinates is in transforming integration questions to make the variables easier to work with. For example, try evaluating

\[ \int_{-\infty}^\infty \int_{-\infty}^\infty e^{x^2+y^2} \, dxdy. \]

As stated in the other discussion started by Shourya:

I don't see why that is an issue. The implicit hint is that you can approach the volume of revolution question via polar coordinates, which would help simplify otherwise strange conditions. Of course, you could do the volume of revolution through normal means, and wade through the ugly integration. Likewise, you could do it via first principles,but that might not be the best approach to use.

Math isn't about sticking to just using certain techniques in certain situations, or memorizing that when you see a question of type X to use standard solution methods Y. You need the flexibility and creativity to apply what you have learnt into novel situations. Especially in the hard set, I try and present various scenarios where it may not be immediately obvious how to approach it, but the hint of the technique should get you started.

Calvin Lin Staff · 3 years, 3 months ago

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I had already started a discussion before. Shourya Pandey · 3 years, 3 months ago

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