Discussion
The heat equation \( z_{t} = \alpha z_{xx} \) is of which type?
Answer: A
Written in the standard form the only second derivative is \( z_{xx} \), so \( A = \alpha \) with \( B = C = 0 \) and
\[ B^{2} - 4AC \;=\; 0, \]
the parabolic case. Parabolic problems march forward in time from an initial state, and their solutions smooth out as they go, which is why heat conduction has no reverse
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