Discussion
Laplace's equation \( z_{xx} + z_{yy} = 0 \) is of which type?
Answer: B
Here \( A = 1 \), \( B = 0 \) and \( C = 1 \), so
\[ B^{2} - 4AC \;=\; 0 - 4 \;=\; -4 \;<\; 0, \]
which is the elliptic case. Elliptic problems carry data on the whole boundary of a closed region and have smooth solutions throughout, with no direction of propagation
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