00:01
In this video, we're going to go through the answer to question number 16 from chapter 10 .2, where we're asked to solve the heat flow problem with the given function f -of -x.
00:13
Okay, so we're told following the theory in the textbook that we have eigenvalues, lambda, is equal to n pi over l, or squared.
00:27
But in this case l is equal to pi, so the icon values are just n squared.
00:34
And the icon functions, un function of x and t, is equal to some constant times by e to the minus beta, which in this case is three, times by lambda squared, which is n squared, t, times by sine n pi over l, which is just n.
01:07
X okay so you the initial condition you at zero well that's going to be equal to the sum of all these eigen functions n equals zero to infinity of cn this e this exponential part is just going to be one so it's times by sign n x and that has to be equal to f of x which is given at the top so there therefore, cn is going to be equal to 1 when n is equal to 3.
02:11
It's going to be 5 when n is equal to 7.
02:17
It's going to be minus 2 when n is equal to 13...