Advanced Engineering Mathematics
Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 14.2, Problem 4E

(a)

To determine

The steady state temperature u(r,z) when u(r,4)=f(r) , 0<r<2 such that the lateral side of the cylinder is insulated.

(b)

To determine

To show: The steady state temperature obtained in sub-part (a) is u(r,z)=u0z4 if f(r)=u0.

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2. (a) State Fermat's principle for the propagation of a light ray from point P at (x1,y1) to Q at (x2, y2), expressing the principle as a problem in Calculus of Variations. (b) Suppose c(y) is the speed of light in a medium, given by c(y) Y where a is a constant. Find the path of a light ray between the points P: (−1,3) and Q (1, 3). Is there more than one possible path? (c) Sketch the path of the light ray, and interpret what an observer at Q would see if there were a light source at P.
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