I have been posed the following question;
The steady-state temperature distribution T on a flat sheet in thexy-plane obeys Laplace’s equation:
. . . . .\(\displaystyle \dfrac{\partial^2 T}{\partial x^2}\, +\, \dfrac{\partial^2 T}{\partial y^2}\, =\, 0\)
(a) Demonstrate that each of the functions
(i) T1(x, y) = e−2ycos 2xand
(ii) T2(x, y) = ln px2 + y2 is a solution to Laplace’s equation.
(b) For each of these two temperature functions, determine the rateof change of the temperature if moving from the location (0, −1)towards the origin.
and I don't know how to preform part a) so I was wondering if someone might be able to walk me through the process?
cheers
The steady-state temperature distribution T on a flat sheet in thexy-plane obeys Laplace’s equation:
. . . . .\(\displaystyle \dfrac{\partial^2 T}{\partial x^2}\, +\, \dfrac{\partial^2 T}{\partial y^2}\, =\, 0\)
(a) Demonstrate that each of the functions
(i) T1(x, y) = e−2ycos 2xand
(ii) T2(x, y) = ln px2 + y2 is a solution to Laplace’s equation.
(b) For each of these two temperature functions, determine the rateof change of the temperature if moving from the location (0, −1)towards the origin.
and I don't know how to preform part a) so I was wondering if someone might be able to walk me through the process?
cheers
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