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--- math121b:04-03 [2020/04/03 09:40]
pzhou
+++ math121b:04-03 [2020/04/03 09:55]
pzhou
@@ Line 61: / Line 61: @@
 ** Case 1: Bottom and Side boundary value = 0. $u(r,\theta,z=1)$ is given **
-Since $R(r)$ will have a zero at $r=1$, we should have $\lambad_r = -k^2 < 0$, and
+Since $R( r)$ will have a zero at $r=1$, we should have $\lambda_r = -k^2 < 0$, and
 $$ u_{k,n}(r, \theta, z) = J_n(kr) \cos(n\theta) \sinh(k z), \quad J_n(kr) \sin(n\theta) \sinh(k z)$$
 For each $n$, we need to choose those $k$ such that $J_n(k 1) = 0$, hence the choice of $k$ is discrete as well.

Lecture Notes