In this video I go over another example on parametric curves as well as discussing how we can write any function as a pair of parametric equations, which we can then graph out. The example I go over is graphing the function x = y^4 -3y^2 which although can be plotted normally, I rewrite it as a pair of parametric equations by setting t = y. Thus the equations become x = t^4 - 3t^2 and y = t. This makes it possible to track a particle as it follows the path of the curve.
In general any function can be written as a pair of differential equations by first setting a parameter t to equal either x or y. Parametric equations makes it possible to graph very complicated, and near impossible to manually sketch, curves. I go over a few of them and show just how amazing some of the curves that can generated. I also use the Desmos online graphing calculator to illustrate how to graph parametric curves and to trace how the particle moves across them.
This is an incredibly cool video on parametric videos, and the amazing graphs that can be produced has been the driving force for me to pursue deeper into mathematics. This is one of my favorite topics, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIht9Y4VpY_aSiv4ytKA
View Video Notes on Steemit: https://steemit.com/steemstem/@mes/parametric-curves-example-6-graphing-devices
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The ability to graph some very amazing curves is why parametric equations are one of my favorite math topics!
View Video Notes: https://steemit.com/steemstem/@mes/parametric-curves-example-6-graphing-devices
@mes this post and your previous post are some very interesting stuff. thank you
Glad you like 'em!!