\magnification=\magstep2

$$
{ {d^2 x}\over{dt^2} } \quad = \quad - {{C}\over{x^2}}
$$

$$
\eqalign{
 { {dv}\over{dt} } \quad &= \quad - {{ K}\over{x^2}}  \cr
 { {dx}\over{dt} } \quad &= \quad  {v} \cr
}
$$

$$
{\rm flow\ in\ from\ left\ } \quad = \quad
          f(x_{i}) \ dy \ dz 
$$

$$
{\rm flow\ out\ to\ right\ } \quad = \quad
          f(x_{i+1}) \ dy \  dz 
$$

$$
 f(x_{i+1})  \ dy \ dz \quad = \quad f(x_i)  \ dy \  dz 
$$

$$
\Delta x \quad \equiv \quad x_{i+1} - x_i 
$$

$$
f(x + \Delta x) \quad = \quad f(x)
$$

$$
{ {\partial f}\over{\partial x} } \quad = \quad 0
$$

$$
{ {\partial f}\over{\partial y} } \quad = \quad 0
$$

$$
f(x) \quad = \quad C \qquad ({\rm some\ constant\ value})
$$

$$
{ {\partial q }\over{\partial x} } \ + \ 
{ {\partial q }\over{\partial y} } 
\quad = \quad 0
$$

$$
{q} \quad = \quad - k {{\partial T} \over{\partial x}}
$$

$$
{{\partial^2 T}\over{\partial x^2}} \quad = \quad 0
$$

$$
{{\partial^2 T}\over{\partial x^2}} \ + \ 
{{\partial^2 T}\over{\partial y^2}} 
\quad = \quad 0
$$

$$
{{\partial^2 T}\over{\partial x^2}} \quad = \quad S(x)
$$

$$
{\rm forward\ difference \ } D^+_i \quad = \quad  
       {{T_{i+1} - T_{i}} \over {x_{i+1} - x_{i} } }
$$

$$
{\rm backward\ difference \ } D^-_i \quad = \quad  
       {{T_{i} - T_{i-1}} \over {x_{i} - x_{i-1} } }
$$

$$
{\rm centered\ second\ difference \ } D^2_{i} \quad = \quad  
       {{D^+_{i} - D^-_{i}} \over {{{1}\over{2}} (x_{i+1} - x_{i-1}) } }
$$

$$
T_{\rm new} \quad = \quad (1 - \lambda)  T_{\rm old} \ + \ \lambda T_{\rm predicted}
$$


\bye


