Remark for your amusement only the isoperimetric

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Unformatted text preview: ose to the boundary of the unit disk. (Please turn in this plot, and give us the values of αj that you find.) The function polyval may be helpful. Remarks. • We’ve been a little informal in our mathematics here, but it won’t matter. • You do not need to know any complex analysis to solve this problem; we’ve told you everything you need to know. • A basic result from complex analysis tells us that ϕ is one-to-one if and only if the image of ˆ the boundary does not ‘loop over’ itself. (We mention this just for fun; we’re not asking you to verify that the ϕ you find is one-to-one.) ˆ 7.12 Fitting a vector field to given directions. This problem concerns a vector field on Rn , i.e., a function F : Rn → Rn . We are given the direction of the vector field at points x(1) , . . . , x(N ) ∈ Rn , q (i) = 1 F ( x (i) ) F ( x (i) ) , i = 1, . . . , N. 2 (These directions might be obtained, for example, from samples of trajectories of the differential equation z = F (z ).) The goal is to fit these samples with a vector field of th...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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