
\magnification=\magstep2


$$
V(t) \quad = \quad V_0 e^{- {{(t - t_0)^2} / { 2 \sigma^2 }} }
$$

$$
\sigma \quad = \quad {{\rm FWHM}\over{2.35}} \quad = \quad 0.426
$$


$$
K^2 \quad = \quad \sum_i{ \left( {{\rm data}_i - {\rm model}_i} \right) ^2} 
$$


$$
f(A, t) \quad = \quad \sum_i{ \left( {{\rm data}_i - 
          { A e^{- {{(t_i - t)^2} / { 2 \sigma^2 }} }  } } \right) ^2}  
$$

$$
\nabla f  \quad = \quad \ {{ \partial f } \over { \partial A }} \hat{\imath} \ +
                 \ {{ \partial f } \over { \partial t }} \hat{\jmath} 
$$

$$
{{\partial f}\over{\partial A}} \quad \simeq \quad
     {{ f(A_1  + \delta A, t_1) - f(A_1 - \delta A, t_1)} \over { 2 \thinspace \delta A }}
$$

$$
{{\partial f}\over{\partial t}} \quad \simeq \quad
     {{ f(A_1, t_1 + \delta t) - f(A_1, t_1 - \delta t)} \over { 2 \thinspace \delta t }}
$$


$$
f(4 + 0.5, 7) \quad = \quad 108
$$

$$
f(4 - 0.5, 7) \quad = \quad 94
$$

$$
f(4, 7 + 0.5) \quad = \quad 4
$$

$$
f(4, 7 - 0.5) \quad = \quad 224
$$

$$
\hat{h} \quad = \quad - \left ( {{14}\over{\sqrt{14^2 + 220^2}}} \right ) \hat{\imath} \ +
                        \left ( {{220}\over{\sqrt{14^2 + 220^2}}} \right ) \hat{\jmath} 
$$

$$
{\rm new\ }(A, t) \quad = \quad (A, t) \ + \ {\rm stepsize} * \hat{h} 
$$




\bye
