.MCAD 304020000 1 74 411 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.218750 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
.CMD COLORTAB_ENTRY 128 128 0
.CMD COLORTAB_ENTRY 0 0 128
.CMD COLORTAB_ENTRY 128 0 128
.CMD COLORTAB_ENTRY 0 128 128
.CMD COLORTAB_ENTRY 128 128 128
.CMD COLORTAB_ENTRY 192 192 192
.CMD COLORTAB_ENTRY 255 0 0
.CMD COLORTAB_ENTRY 0 255 0
.CMD COLORTAB_ENTRY 255 255 0
.CMD COLORTAB_ENTRY 0 0 255
.CMD COLORTAB_ENTRY 255 0 255
.CMD COLORTAB_ENTRY 0 255 255
.CMD COLORTAB_ENTRY 255 255 255
.EQN 2 1 41 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 3 42 0 0
Cg a69.000000,69.000000,66
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green128\blue128;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b Page 
MC-23  MATHEMATICAL SOFTWARE PACKAGES IN CHEMICAL ENGINEERING}}
.EQN 1 -3 43 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 3 44 0 0
Cg a69.000000,69.000000,30
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green128\blue128;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b 
Mathcad Solution to Problem 10}}
.TXT 3 -2 46 0 0
Cg a72.000000,72.000000,93
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard The solutions to this 
problem make use of the differential equation solver built into Mathcad}
.TXT 5 0 48 0 0
Cg a72.000000,72.000000,75
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Define physical 
properties of the system as given in the problem statement.}
.EQN 4 4 1 0 0
{0:\rVC.p}NAME:4000
.EQN 0 24 7 0 0
{0:WC.p}NAME:500
.TXT 5 -24 64 0 0
Cg a68.000000,68.000000,18
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Inlet temperature:}
.EQN 0 14 65 0 0
{0:T.is}NAME:60
.TXT 0 10 67 0 0
Cg a44.000000,44.000000,22
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Set point temperature:}
.EQN 0 18 68 0 0
{0:T.r}NAME:80
.TXT 4 -42 147 0 0
Cg a68.000000,68.000000,14
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Tank dead time}
.EQN 0 14 148 0 0
{0:\t.d}NAME:1
.TXT 0 10 149 0 0
Cg a44.000000,44.000000,27
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Thermocouple time constant:}
.EQN 0 23 150 0 0
{0:\t.m}NAME:5
.TXT 4 -47 151 0 0
Cg a68.000000,68.000000,16
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Controller gain:}
.EQN 0 14 152 0 0
{0:K.C}NAME:2
.TXT 0 10 153 0 0
Cg a44.000000,44.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Controller integral time:}
.EQN 0 23 154 0 0
{0:\t.I}NAME:2
.TXT 5 -51 86 0 0
Cg a68.000000,68.000000,34
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Calculate steady state 
heat input:}
.EQN 0 28 87 0 0
{0:q.s}NAME:{0:WC.p}NAME*({0:T.r}NAME-{0:T.is}NAME)
.TXT 6 -28 98 0 0
Cg a72.000000,72.000000,51
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Define the heat input 
calculated by the controller:}
.EQN 0 38 100 0 0
{0:q}NAME({0:T.m}NAME,{0:e}NAME):{0:q.s}NAME+{0:K.C}NAME*({0:T.r}NAME-{0:T.m}NAME)+({0:K.C}NAME)/({0:\t.I}NAME)*{0:e}NAME
.TXT 4 -38 88 0 0
Cg a73.000000,73.000000,154
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Mathcad requires the 
unknown variables to be expressed as a vector.  We will define the 
variables as follows:\tab T = x{\dn 0}, T0 = x{\dn 1}, Tm = x{\dn 2}, 
and errsum = x{\dn 3}   }
.TXT 7 0 54 0 0
Cg a72.000000,72.000000,166
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b a) Open Loop Performance}
\par \par The step change in inlet temperature is represented in 
Mathcad by defining the inlet temperature as a function of time using 
an {\i if} function.}
.EQN 10 5 55 0 0
{0:Ti}NAME({0:t}NAME):{0:if}NAME({0:t}NAME<10,{0:T.is}NAME,{0:T.is}NAME-20)
.TXT 5 -5 89 0 0
Cg a72.000000,72.000000,59
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard For open loop 
performance, set the controller gain to zero.}
.EQN 0 48 90 0 0
{0:K.c}NAME:0
.TXT 4 -48 92 0 0
Cg a72.000000,72.000000,75
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Define the vector of 
functions representing the right hand side of the ODEs}
.EQN 13 5 104 0 0
{0:D}NAME({0:t}NAME,{0:x}NAME):({4,1}ö{0:T.r}NAME-({0:x}NAME)[(2)ö(({0:x}NAME)[(1)-({0:x}NAME)[(2))/({0:\t.m}NAME)ö(({0:x}NAME)[(0)-({0:x}NAME)[(1)-({0:\t.d}NAME)/(2)*(({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),(
{0:x}NAME)[(3)))/({0:\rVC.p}NAME)))*(2)/({0:\t.d}NAME)ö({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),({0:x}NAME)[(3)))/({0:\rVC.p}NAME))
.TXT 12 -6 113 0 0
C x1,1,0,0
.EQN 2 0 110 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 3 111 0 0
Cg a69.000000,69.000000,66
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green128\blue128;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b Page 
MC-24  MATHEMATICAL SOFTWARE PACKAGES IN CHEMICAL ENGINEERING}}
.EQN 1 -3 112 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 2 116 0 0
Cg a71.000000,71.000000,19
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Initial conditions:}
.TXT 0 29 127 0 0
Cg a42.000000,42.000000,13
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Initial time:}
.EQN 0 11 128 0 0
{0:t.0}NAME:0
.TXT 3 -11 129 0 0
Cg a42.000000,42.000000,11
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Final time:}
.EQN 0 11 130 0 0
{0:t.f}NAME:60
.EQN 2 -24 117 0 0
{0:x}NAME:({4,1}ö0ö{0:T.r}NAMEö{0:T.r}NAMEö{0:T.r}NAME)
.TXT 1 13 131 0 0
Cg a42.000000,42.000000,10
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Time step:}
.EQN 0 11 132 0 0
{0:\Dt}NAME:0.1
.EQN 4 -11 133 0 0
{0:npoints}NAME:({0:t.f}NAME-{0:t.0}NAME)/({0:\Dt}NAME)+1
.EQN 0 20 135 0 0
{0:i}NAME:1;{0:npoints}NAME
.TXT 5 -50 136 0 0
Cg a72.000000,72.000000,62
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Solve the system of ODEs 
using the adaptive Runge-Kutta method}
.EQN 4 3 134 0 0
{0:Z}NAME:{0:Rkadapt}NAME({0:x}NAME,{0:t.0}NAME,{0:t.f}NAME,{0:npoints}NAME,{0:D}NAME)
.TXT 5 -3 138 0 0
Cg a70.000000,70.000000,59
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Assign columns of the 
solution array to vectors for clarity}
.EQN 4 3 139 0 0
({0:t}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,0)
.EQN 0 10 140 0 0
({0:T}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,1)
.EQN 0 11 143 0 0
({0:T.0}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,2)
.EQN 0 13 144 0 0
({0:T.m}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,3)
.EQN 0 12 145 0 0
({0:errsum}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,4)
.EQN 4 -50 146 0 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:T}NAME)[({0:i}NAME),({0:T.0}NAME)[({0:i}NAME),({0:T.m}NAME)[({0:i}NAME)@{0:t.f}NAME&&(_n_u_l_l_&_n_u_l_l_)&({0:t}NAME)[({0:i}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 3 1 0 1 1 NO-TRACE-STRING
0 1 6 0 2 2 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 61 32 10 0 3 
.TXT 42 0 155 0 0
C x1,1,0,0
.EQN 1 0 161 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 3 162 0 0
Cg a69.000000,69.000000,66
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green128\blue128;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b Page 
MC-25  MATHEMATICAL SOFTWARE PACKAGES IN CHEMICAL ENGINEERING}}
.EQN 1 -3 163 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 1 164 0 0
Cg a72.000000,72.000000,26
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b b) Closed loop performance}}
.TXT 3 0 200 0 0
Cg a68.000000,68.000000,16
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Controller gain:}
.TXT 0 15 211 0 0
Cg a44.000000,44.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Controller integral time:}
.EQN 3 -13 210 0 0
{0:K.C}NAME:50
.EQN 0 18 213 0 0
{0:\t.I}NAME:2
.EQN 0 21 208 0 0
{0:q}NAME({0:T.m}NAME,{0:e}NAME):{0:q.s}NAME+{0:K.C}NAME*({0:T.r}NAME-{0:T.m}NAME)+({0:K.C}NAME)/({0:\t.I}NAME)*{0:e}NAME
.TXT 6 -41 196 0 0
Cg a72.000000,72.000000,75
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Define the vector of 
functions representing the right hand side of the ODEs}
.EQN 13 4 175 0 0
{0:D}NAME({0:t}NAME,{0:x}NAME):({4,1}ö{0:T.r}NAME-({0:x}NAME)[(2)ö(({0:x}NAME)[(1)-({0:x}NAME)[(2))/({0:\t.m}NAME)ö(({0:x}NAME)[(0)-({0:x}NAME)[(1)-({0:\t.d}NAME)/(2)*(({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),(
{0:x}NAME)[(3)))/({0:\rVC.p}NAME)))*(2)/({0:\t.d}NAME)ö({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),({0:x}NAME)[(3)))/({0:\rVC.p}NAME))
.TXT 14 -4 197 0 0
Cg a71.000000,71.000000,19
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Initial conditions:}
.TXT 0 29 177 0 0
Cg a42.000000,42.000000,13
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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.EQN 0 11 178 0 0
{0:t.0}NAME:0
.TXT 3 -11 179 0 0
Cg a42.000000,42.000000,11
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Final time:}
.EQN 0 11 180 0 0
{0:t.f}NAME:200
.EQN 2 -24 181 0 0
{0:x}NAME:({4,1}ö0ö{0:T.r}NAMEö{0:T.r}NAMEö{0:T.r}NAME)
.TXT 1 13 182 0 0
Cg a42.000000,42.000000,10
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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.EQN 0 11 183 0 0
{0:\Dt}NAME:0.1
.EQN 4 -11 184 0 0
{0:npoints}NAME:({0:t.f}NAME-{0:t.0}NAME)/({0:\Dt}NAME)+1
.EQN 0 20 185 0 0
{0:i}NAME:1;{0:npoints}NAME
.TXT 4 -50 186 0 0
Cg a72.000000,72.000000,62
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Solve the system of ODEs 
using the adaptive Runge-Kutta method}
.EQN 3 3 187 0 0
{0:Z}NAME:{0:Rkadapt}NAME({0:x}NAME,{0:t.0}NAME,{0:t.f}NAME,{0:npoints}NAME,{0:D}NAME)
.TXT 4 -3 188 0 0
Cg a70.000000,70.000000,59
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Assign columns of the 
solution array to vectors for clarity}
.EQN 3 3 189 0 0
({0:t}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,0)
.EQN 0 10 190 0 0
({0:T}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,1)
.EQN 0 11 191 0 0
({0:T.0}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,2)
.EQN 0 13 192 0 0
({0:T.m}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,3)
.EQN 0 12 193 0 0
({0:errsum}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,4)
.EQN 2 -49 198 0 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:T}NAME)[({0:i}NAME),({0:T.0}NAME)[({0:i}NAME),({0:T.m}NAME)[({0:i}NAME),{0:T.r}NAME@{0:t.f}NAME&&(_n_u_l_l_&_n_u_l_l_)&({0:t}NAME)[({0:i}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 3 1 0 1 1 NO-TRACE-STRING
0 1 6 0 2 2 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 62 21 10 0 3 
.TXT 28 0 244 0 0
C x1,1,0,0
.EQN 1 0 214 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 3 215 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green128\blue128;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b Page 
MC-26  MATHEMATICAL SOFTWARE PACKAGES IN CHEMICAL ENGINEERING}}
.EQN 1 -3 216 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 1 217 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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performance - increasing K}{\b\dn C}{\b  to 500}}
.TXT 3 0 218 0 0
Cg a68.000000,68.000000,16
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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.TXT 0 15 219 0 0
Cg a44.000000,44.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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.EQN 3 -13 220 0 0
{0:K.C}NAME:500
.EQN 0 18 221 0 0
{0:\t.I}NAME:2
.EQN 0 21 222 0 0
{0:q}NAME({0:T.m}NAME,{0:e}NAME):{0:q.s}NAME+{0:K.C}NAME*({0:T.r}NAME-{0:T.m}NAME)+({0:K.C}NAME)/({0:\t.I}NAME)*{0:e}NAME
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Define the vector of 
functions representing the right hand side of the ODEs}
.EQN 13 4 224 0 0
{0:D}NAME({0:t}NAME,{0:x}NAME):({4,1}ö{0:T.r}NAME-({0:x}NAME)[(2)ö(({0:x}NAME)[(1)-({0:x}NAME)[(2))/({0:\t.m}NAME)ö(({0:x}NAME)[(0)-({0:x}NAME)[(1)-({0:\t.d}NAME)/(2)*(({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),(
{0:x}NAME)[(3)))/({0:\rVC.p}NAME)))*(2)/({0:\t.d}NAME)ö({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),({0:x}NAME)[(3)))/({0:\rVC.p}NAME))
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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.TXT 0 29 226 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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.EQN 0 11 227 0 0
{0:t.0}NAME:0
.TXT 3 -11 228 0 0
Cg a42.000000,42.000000,11
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Final time:}
.EQN 0 11 229 0 0
{0:t.f}NAME:200
.EQN 2 -24 230 0 0
{0:x}NAME:({4,1}ö0ö{0:T.r}NAMEö{0:T.r}NAMEö{0:T.r}NAME)
.TXT 1 13 231 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Time step:}
.EQN 0 11 232 0 0
{0:\Dt}NAME:0.1
.EQN 4 -11 233 0 0
{0:npoints}NAME:({0:t.f}NAME-{0:t.0}NAME)/({0:\Dt}NAME)+1
.EQN 0 20 234 0 0
{0:i}NAME:1;{0:npoints}NAME
.TXT 4 -50 235 0 0
Cg a72.000000,72.000000,62
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Solve the system of ODEs 
using the adaptive Runge-Kutta method}
.EQN 3 3 236 0 0
{0:Z}NAME:{0:Rkadapt}NAME({0:x}NAME,{0:t.0}NAME,{0:t.f}NAME,{0:npoints}NAME,{0:D}NAME)
.TXT 4 -3 237 0 0
Cg a70.000000,70.000000,59
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Assign columns of the 
solution array to vectors for clarity}
.EQN 3 3 238 0 0
({0:t}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,0)
.EQN 0 10 239 0 0
({0:T}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,1)
.EQN 0 11 240 0 0
({0:T.0}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,2)
.EQN 0 13 241 0 0
({0:T.m}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,3)
.EQN 0 12 242 0 0
({0:errsum}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,4)
.EQN 2 -49 243 0 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:T}NAME)[({0:i}NAME),({0:T.0}NAME)[({0:i}NAME),({0:T.m}NAME)[({0:i}NAME),{0:T.r}NAME@{0:t.f}NAME&&(_n_u_l_l_&_n_u_l_l_)&({0:t}NAME)[({0:i}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 3 1 0 1 1 NO-TRACE-STRING
0 1 6 0 2 2 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 62 21 10 0 3 
.TXT 28 0 245 0 0
C x1,1,0,0
.EQN 1 0 246 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 3 247 0 0
Cg a69.000000,69.000000,66
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green128\blue128;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b Page 
MC-27  MATHEMATICAL SOFTWARE PACKAGES IN CHEMICAL ENGINEERING}}
.EQN 1 -3 248 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 1 249 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b d) Closed loop 
performance - Proportional only controller}}
.TXT 3 0 250 0 0
Cg a68.000000,68.000000,16
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Controller gain:}
.TXT 0 15 251 0 0
Cg a44.000000,44.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Controller integral time:}
.EQN 3 -13 252 0 0
{0:K.C}NAME:500
.EQN 0 18 253 0 0
{0:\t.I}NAME:0
.EQN 0 21 254 0 0
{0:q}NAME({0:T.m}NAME,{0:e}NAME):{0:q.s}NAME+{0:K.C}NAME*({0:T.r}NAME-{0:T.m}NAME)
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Define the vector of 
functions representing the right hand side of the ODEs}
.EQN 13 4 256 0 0
{0:D}NAME({0:t}NAME,{0:x}NAME):({4,1}ö{0:T.r}NAME-({0:x}NAME)[(2)ö(({0:x}NAME)[(1)-({0:x}NAME)[(2))/({0:\t.m}NAME)ö(({0:x}NAME)[(0)-({0:x}NAME)[(1)-({0:\t.d}NAME)/(2)*(({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),(
{0:x}NAME)[(3)))/({0:\rVC.p}NAME)))*(2)/({0:\t.d}NAME)ö({0:WC.p}NAME*({0:Ti}NAME({0:t}NAME)-({0:x}NAME)[(0))+{0:q}NAME(({0:x}NAME)[(2),({0:x}NAME)[(3)))/({0:\rVC.p}NAME))
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
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.TXT 0 29 258 0 0
Cg a42.000000,42.000000,13
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Initial time:}
.EQN 0 11 259 0 0
{0:t.0}NAME:0
.TXT 3 -11 260 0 0
Cg a42.000000,42.000000,11
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Final time:}
.EQN 0 11 261 0 0
{0:t.f}NAME:60
.EQN 2 -24 262 0 0
{0:x}NAME:({4,1}ö0ö{0:T.r}NAMEö{0:T.r}NAMEö{0:T.r}NAME)
.TXT 1 13 263 0 0
Cg a42.000000,42.000000,10
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Time step:}
.EQN 0 11 264 0 0
{0:\Dt}NAME:0.1
.EQN 4 -11 265 0 0
{0:npoints}NAME:({0:t.f}NAME-{0:t.0}NAME)/({0:\Dt}NAME)+1
.EQN 0 20 266 0 0
{0:i}NAME:1;{0:npoints}NAME
.TXT 4 -50 267 0 0
Cg a72.000000,72.000000,62
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Solve the system of ODEs 
using the adaptive Runge-Kutta method}
.EQN 3 3 268 0 0
{0:Z}NAME:{0:Rkadapt}NAME({0:x}NAME,{0:t.0}NAME,{0:t.f}NAME,{0:npoints}NAME,{0:D}NAME)
.TXT 4 -3 269 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Assign columns of the 
solution array to vectors for clarity}
.EQN 3 3 270 0 0
({0:t}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,0)
.EQN 0 10 271 0 0
({0:T}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,1)
.EQN 0 11 272 0 0
({0:T.0}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,2)
.EQN 0 13 273 0 0
({0:T.m}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,3)
.EQN 0 12 274 0 0
({0:errsum}NAME)[({0:i}NAME):({0:Z}NAME)[({0:i}NAME,4)
.EQN 2 -49 275 0 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:T}NAME)[({0:i}NAME),({0:T.0}NAME)[({0:i}NAME),({0:T.m}NAME)[({0:i}NAME),{0:T.r}NAME@{0:t.f}NAME&&(_n_u_l_l_&_n_u_l_l_)&({0:t}NAME)[({0:i}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 3 1 0 1 1 NO-TRACE-STRING
0 1 6 0 2 2 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 62 21 10 0 3 
.TXT 28 0 276 0 0
C x1,1,0,0
.EQN 1 0 281 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 3 282 0 0
Cg a69.000000,69.000000,66
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green128\blue128;}{
\fonttbl{\f0\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\cf2\b Page 
MC-28  MATHEMATICAL SOFTWARE PACKAGES IN CHEMICAL ENGINEERING}}
.EQN 1 -3 283 0 0
{    8   580 0 0}{61}
19778 4560 0 0 1068
40 580 6 1 8 0 3480 0 0 0 0
!!!!!!!!6k!!6k!!!)"C!)!!!!"C!)!!6s!!!-#%Aa#%FW!!I}>!!%87>{"cAn6kDU#U!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!J"A`!+-Y<7"C6s!!!!#d!!#d!!!!LVIqLG!!!0IqLG#dLG!!LVLV!!4'5hLVLVJYLG4'5hLVLVJYLG>{5Y)0LG.Z!e)5!@I|!(9SLVIuLG,Z!a&J"3"<LVLVLK4&"3"<LVLVLK4&

.TXT 4 1 284 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b e) Closed loop 
performance - Heater output limited}}
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