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Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} andthat U(1, θ) = 5 − sin2θ.(i) Without finding the solution to the equation, compute the value of U at theorigin – i.e. at r = 0.(ii) Without finding the solution to the equation, determine the location of themaxima and minima of U in Ω.(Hint: sin2θ =(1−cos 2θ)/2.)

Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} andthat U(1, θ) = 5 − sin2θ.(i) Without finding the solution to the equation, compute the value of U at theorigin – i.e. at r = 0.(ii) Without finding the solution to the equation, determine the location of themaxima and minima of U in Ω.(Hint: sin2θ =(1−cos 2θ)/2.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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 Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} and
that U(1, θ) = 5 − sin2θ.
(i) Without finding the solution to the equation, compute the value of U at the
origin – i.e. at r = 0.
(ii) Without finding the solution to the equation, determine the location of the
maxima and minima of U in Ω.
(Hint: sin2θ =(1−cos 2θ)/2.)

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