4. Boas Chapter 13 section 7 number 11

___ CI ' ___ ______' _____J._ ___'____ __ __ _" " ____ "' 3' _' __ ___ The temperature of the equatorial plane 9 = 7r/2 or cosl = 0 as given by equa- tions (7.11) to (7.15) is halfway between the top and bottom surface temperatures, because Legendre series, like Fourier series, converge to the midpoint of a jump in the function which was expanded to get the series. To solve the problem of the temperature in a hemisphere given the temperatures of the curved surface and of the equatorial plane, we need only imagine the lower hemisphere in place and at the proper temperature to give the desired average on the equatorial plane. When the temperature of the equatorial plane is 0, this amounts to dening the function f(:z:) in (7.13) on (1,0) to make it an odd functiOn. 11. Find the steadystate temperature distribution inside a hemisphere if the spherical surface is held at 100 and the equatorial plane at 0. Hint: See the last paragraph of this section above