PPT Slide
Partial Differential Equations (PDE): Many physical phenomena are
governed by PDE since the physical functions involved usually depend on two
or more independent variables (ex. Time, spatial coordinates). Their variation with
respect to these variables need to be described by PDE not ODE (Ordinary
Example: In dynamics, we often track the change of the position of an object
in time. Time is the only variable in this case. X=x(t), u=dx/dt, a=du/dt.
In heat transfer, temperature inside an object can vary with both time and space.
T=T(x,t). The temperature varies with time since it has not reach its thermal
The temperature can also vary in space as according to the Fourier’s law: