HEAD  PREVIOUS 
∫_{0}^{xn}f(x)dx=y_{n}−y_{0}= 
n−1 ∑ k=0  f(x_{k+1/2})(x_{k+1}−x_{k}) 
∆y = (^{1}/_{6}F(0)+^{1}/_{3}F( 
∆
 ) +^{1}/_{3}F( 
∆
 )+^{1}/_{6}F(∆))∆ 
∆

∂f

f^{(1)}−F( 
∆
 )= 
∂f
 (y^{(1)}−y( 
∆
 )) 
f^{(2)}−F( 
∆
 )= 
∂f
 (y^{(2)}−y( 
∆
 )) 
f^{(3)}−F(∆)= 
∂f
 (y^{(3)}−y(∆)) 
∂^{2}

(y^{(1)}−y( 
∆
 )) 
∂f


d^{2}y
 =0 
∑  y_{n}/N=0 
∆x^{2}(g− 
∑  g_{n} /N) 
N ∑ 1  (v_{i}−μ_{N})^{2} 


N!



f_{k}d^{3}v_{k} = 
∑ v_{i} ∈ d^{3}v_{k}  ∆t_{i} 

1 Initialize:  choose x_{0}, r_{0}=b−Ax_{0},
p_{0}=r_{0}, choose
,
, set k=1.  
2 Calculate α: 
 
3 Update rs, x:  r_{k} = r_{k−1} − α_{k−1} Ap_{k−1},
,  
x_{k}=x_{k−1} − α_{k−1} Ap_{k−1}.  
4 Calculate β: 
 
5 Update ps:  p_{k}=r_{k}−β_{k,k−1}p_{k−1}
and
 
6 Convergence?  If not converged, increment k and repeat from 2. 
0= 
∂ρ
 =−∇.(ρv) 