3 7.24, §3 Transform

Transform the PDE:

$$\strut u_t = \kappa u_{xx} \quad \stackrel{\hbox{Table 6.3... ...u - \overline{\smash{u(x,0)}\vphantom{.}} = \kappa \hat u_{xx}$$

Transform the BC:

$$u_x = g(t) \quad \Relbar\joinrel\Relbar\joinrel\Relbar\... ...l \Relbar\joinrel\Longrightarrow \quad \hat u_x = \hat g(s)$$