Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} and that U(1, θ) = 5 − sin^2(θ). (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: sin^2(θ) =(1−cos^2(θ))/2.)

Suppose that U is a solution to the Laplace equation in the disk Ω = {r ≤ 1} and that U(1, θ) = 5 − sin^2(θ). (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: sin^2(θ) =(1−cos^2(θ))/2.)

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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