3 7.36, §3 Transform

Transform the PDE:

$$u_{xx} = a^2 u_{yy} \quad \stackrel{\hbox{Table 6.3, \char... ... - \overline{\smash{u_x(0,y)}\vphantom{.}} = a^2 \hat u_{yy}$$

Transform the BC:

$$u_y - p u = f(x) \quad \Relbar\joinrel\Relbar\joinrel\R... ...joinrel\Longrightarrow \quad \hat u_y - p \hat u = \hat f(s)$$