(0:00) Lecture plan. (0:47) Use Mathematica to make interactive graphics, ultimately using Manipulate, Graphics3D, and Cylinder to make an interactive cylinder that can change in radius and height. Make use of the Wolfram documentation for examples. (9:17) Minimize the surface area of an open cylinder (with the top missing) when the volume is fixed (find the optimal radius and height to minimize the surface area). (23:14) Minimize the sum of the distances between two towns and a water pumping station along a straight river (for the purposes of minimizing the total cost of piping). Do this in the general case, which involves some complicated calculations, but which amazingly reduces to a pretty nice final result. Show the final graph with Manipulate on Mathematica.
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(0:00) Lecture plan. (0:47) Use Mathematica to make interactive graphics, ultimately using Manipulate, Graphics3D, and Cylinder to make an interactive cylinder that can change in radius and height. Make use of the Wolfram documentation for examples. (9:17) Minimize the surface area of an open cylinder (with the top missing) when the volume is fixed (find the optimal radius and height to minimize the surface area). (23:14) Minimize the sum of the distances between two towns and a water pumping station along a straight river (for the purposes of minimizing the total cost of piping). Do this in the general case, which involves some complicated calculations, but which amazingly reduces to a pretty nice final result. Show the final graph with Manipulate on Mathematica.
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