Did you know that bubbles are actually really good at math? Everytime an object is dipped in bubble solution, the bubble has to solve a differential equation to figure out the shape it will take while lying on that object. That differential equation is:
\[ (1 + u_x^2)u_{yy} -2u_xu_yu_{xy} + (1 + u_y^2)u_{xx} = 0 \]
This differential equation is incredibly difficult for any human to solve, and as a result there are are not that many well defined examples of minimal surfaces.
Throughout the semester we have covered a variety of topics and how their mathematical orientation applies to real world scenarios. One topic we discussed, and I would like to revisit, is integration over a region in a plane which involves calculating a double integral. Integrating functions of two variables allows us to calculate the volume under the function in a 3D space. You can see a more in depth description and my previous example in my blog post, https://ukyma391.blogspot.com/2021/09/integration-for-over-regions-in-plane_27.html . I want to revisit this topic because in my previous attempt my volume calculations were incorrect, and my print lacked structural stability. I believed this print and calculation was the topic I could most improve on and wanted to give it another chance. What needed Improvement? The function used previously was f(x) = cos(xy) bounded on [-3,3] x [-1,3]. After solving for the estimated and actual volume, it was difficult to represent in a print...
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