
109Introduction to Kinetics and Chemical Reactors
∂
∂
=++−
====
∑∑∑∑
J
a
axaxxa xyx
iii
i
N
i
i
N
ii
i
N
i
N
1
11
2
212
1
01
1
1
11
2
= 0
(B.10)
∂
∂
=++−
==
∑∑
J
a
axxa xaxyx
ii
i
N
ii
i
N
ii
i
N
i
N
2
112
1
22
2
02
1
2
11
2
= 0
(B.11)
Equations B.9, B.10 and B.11 are linear simultaneous equations written in the matrix
form as
(B.12)
where
A
Nxx
xxxx
xx
i
i
N
i
i
N
i
i
N
i
i
N
ii
i
N
i
i
N
i
=
==
===
=
∑∑
∑∑∑
∑
1
1
2
1
1
1
1
2
1
12
1
2
1
1
xxx
X
a
a
a
i
i
N
i
i
N
2
1
2
2
1
0
1
2
==
∑∑
=
;
=
=
=
=
∑
∑
∑
; b
y
xy
xy
i
i
N
ii
i
N
ii
i
N
1
1
1
2
1
(B.13)
Coefcients a
0
, a
1
and a
2
are estimated by solving Equation B.13.
If the problem is to t the data to a linear equation of the type y = a
1
x
1
+ a
2
x
2
, then the
coefcients ...