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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 onetoone 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 onetoone.)
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.
 Fall '13
 F.Borrelli
 The Aeneid

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