Multivariable calculus rogawski11/27/2023 If time permits, do some basic research on “fluid dynamics.” Read the text and do the 12 exercises presented. Anton explores how one can model hurricanes using what we’ve learned thus far (p. vector valued functions, vector fields, etc.). In such a course, you’ll learn that gases can be model as fluids, and some of the beasts we’ve encountered in Multivariable Calculus will rear their heads again (e.g. (2) Hurricane Modeling: In higher mathematics, you can take courses on “fluid dynamics” - how fluids move. UPDATE: a student did this in the 2012/13 class extensively UPDATE: a student did this in the 2009/10 class (but not in super detail, so it could be fleshed out) Perhaps if you can, expand this idea by calculating the surface area of spheres in -dimensions. In fact, as the dimension increases, the volume gets closer and closer to 0. It turns out that the volume of a 5th dimensional sphere of radius 1 will be a maximum, and then the volume of 6th, 7th, 8th, … dimensional spheres will be less. Using what we know about multivariable calculus, believe it or not, it is relatively easy to calculate the volume of an -dimensional sphere. Well, we can talk about a sphere in -dimensions by defining it like. ![]() ![]() (1) The Volume of the Sphere in Higher Dimensions. Feel free to choose one and expand on it, or pick something on your own and (through consultation with me) run with it! The fundamental thing you need to think about when choosing a topic is: does this excite me? If it doesn’t, if you don’t get the sense of “oh my gosh, I can’t wait to start working on this,” you should think twice about choosing it. ![]() Below are ideas for your fourth quarter projects.
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