Question
a.
\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=\frac{∂^2 \overline{u}}{∂r^2}+\frac{1}{r} \frac{∂\overline{u}}{∂r}-\frac{1}{r^2}\frac{∂^2 \overline{u}}{∂θ^2}\)
b.
\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=\frac{∂^2 \overline{u}}{∂r^2}+\frac{1}{r} \frac{∂\overline{u}}{∂r}+\frac{1}{r^2}\frac{∂^2 \overline{u}}{∂θ^2}\)
c.
\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=\frac{∂^2 \overline{u}}{∂r^2}-\frac{1}{r} \frac{∂\overline{u}}{∂r}-\frac{1}{r^2}\frac{∂^2 \overline{u}}{∂θ^2}\)
d.
\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=\frac{∂^2 \overline{u}}{∂r^2}-\frac{1}{r} \frac{∂\overline{u}}{∂r}+\frac{1}{c^2}\frac{∂^2 \overline{u}}{∂θ^2}\)
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Q. The term \(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}\) in terms of r and θ is given by _______
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