\magnification=\magstep1


$$
  y_{i+1} \quad = \quad y_i \ + \ v_i dt
$$

$$
  y_{i+1} \quad = \quad y_i \ + \ v_{i+1} dt
$$


$$
  y_{i+1} \quad = \quad y_i \ + \ 0.5 (v_i + v_{i+1}) dt 
$$

$$
  y_{i+1} \quad = \quad y_i \ + \ 
      {{1}\over{6}}  (k_1 + 2 k_2 + 2 k_3 + k_4) dt
$$

$$
\eqalign{
E_0 \quad &= \quad KE \ + \ GPE  \cr
        & \phantom{=} \cr
        &= \ {{1}\over{2}} m v_0^2 \ - \ {{G M_E m}\over{(R_E + H)} } \cr
}
$$

$$
f \quad \equiv \quad \left | {{E_f - {E_0}}\over{E_0}} \right |
$$

$$
  \log(f) \quad = \quad a \ + \ b \thinspace \log(dt)
$$

$$
  f \quad = \quad 10^a \thinspace  (dt)^b
$$



\bye
