.MCAD 304020000 1 79 813 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 1.000000 1.000000 1.000000 1.000000 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
.CMD COLORTAB_ENTRY 10 36 106
.TXT 3 20 2 0 0
Cg a27.000000,27.000000,28
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\fs28\b EG31 MATHCAD 
NOTES\par SESSION 2}}
.TXT 6 -19 290 0 0
Cg a76.500000,76.500000,472
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Symbolic Calculations}
\par \tab \par \pard \tab Mathcad can perform a number of operations 
which are found in the {\b\ul S}{\b ymbolics }pull-down menu.  The 
results of these operations are generally another expression.  Here 
are examples of some of these operations:\par \pard \par \tab \tab 
\tab \par \tab {\b\ul E}{\b valuate\par \par \tab \tab }{\b To 
evaluate a derivative symbolically\par \par }\pard {\b \tab }1.  
Select the differential operator by selecting  the{\b  d/dx} operator 
from the Math palette or  typing a {\b ?\par }\pard {\b \tab \tab \tab 
\tab }\par \tab \tab \tab \tab \tab \tab \tab \tab {\object{
\*\objclass \eqn}\rsltpict{\*\objdata 
.EQN 38 56 125 0 0
_n_u_l_l_"_n_u_l_l_
}}\par \pard \par \pard \tab 2.  Type the differential expression into 
the placeholders }
.EQN 41 24 789 0 0
{0:z}NAME"(((\({0:z}NAME))/(1+{0:z}NAME)))^(2)
.TXT 5 -24 292 0 0
Cg a76.375000,76.375000,279
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 3.  Select it by 
pressing the space bar or the arrow keys until the editing lines are 
across the complete bottom and right sides or drawing the mouse 
diagonally over the expression.\par \par \pard \tab 4.  Choose {\b\ul E}{
\b valuate} => {\b\ul S}{\b ymbolically} from the {\b\ul S}{\b ymbolics} 
menu. \par \par Mathcad returns the answer:    }
.EQN 17 23 438 0 0
({0}1)/((({0}1+{0:z}NAME))^({0}2))-{0}2*({0:z}NAME)/((({0}1+{0:z}NAME))^({0}3))
.TXT 9 -23 439 0 0
Cg a77.000000,77.000000,310
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab \tab \tab \tab 
Mathcad places the evaluated expression into the worksheet.  The 
location of the evaluated expression can be changed by selecting its 
math region and dragging it to the desire location. The location can 
also be pre-selected based on the Evaluation Style selected.  This 
will not be covered in these notes. }
.TXT 30 0 328 0 0
Cg a76.500000,76.500000,269
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab {\b To evaluate a 
definite integral symbolically\par }\par \pard \tab 1.  Select the 
definite integral operator from the Math palette and fill in the 
placeholders with numerical limits and the expression.  Hint: either 
type the {\b sin(x)} or select the {\b sin} function from the 
Arithmetic palette.\par }
.EQN 18 23 338 0 0
(0&({0:\p}NAME)/(2)`(1)/(1+{0:sin}NAME({0:x}NAME))&{0:x}NAME)
.TXT 7 -23 330 0 0
Cg a77.000000,77.000000,127
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Select the 
complete expression and choose  {\b\ul E}{\b valuate} => {\b\ul S}{\b 
ymbolically} from the {\b\ul S}{\b ymbolics} menu. \par \par Mathcad 
returns the answer:}
.EQN 8 26 331 0 0
{0}1
.TXT 6 -26 332 0 0
Cg a75.875000,75.875000,161
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab \tab An alternate 
method for the solution to a definite integral is to type the  " {\b =} 
"  sign after the expression and press the Enter key to complete the 
operation:}
.EQN 12 21 333 0 0
(0&({0:\p}NAME)/(2)`(1)/(1+{0:sin}NAME({0:x}NAME))&{0:x}NAME)={0}?_n_u_l_l_
.TXT 8 -21 334 0 0
Cg a76.250000,76.250000,235
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b \tab To evaluate an 
integral with symbolic limits, symbolically}\par \par \pard \tab 1.  
Select the definite integral operator from the Math palette and fill 
in the placeholders with variables for the limits of integration and 
the expression to be integrated}
.EQN 13 21 335 0 0
({0:a}NAME&{0:t}NAME`(1)/(1+{0:sin}NAME({0:x}NAME))&{0:x}NAME)
.TXT 8 -21 336 0 0
Cg a77.000000,77.000000,127
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Select the 
complete expression and choose  {\b\ul E}{\b valuate} => {\b\ul S}{\b 
ymbolically} from the {\b\ul S}{\b ymbolics} menu. \par \par \pard 
Mathcad returns the answer:}
.EQN 11 20 337 0 0
(-{0}2)/(({0}1+{0:tan}NAME(({0}1)/({0}2)*{0:t}NAME)))+({0}2)/(({0}1+{0:tan}NAME(({0}1)/({0}2)*{0:a}NAME)))
.TXT 16 -20 490 0 0
Cg a76.375000,76.375000,228
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b To evaluate an 
indefinite integral symbolically}\par \par \pard \tab 1.  Select the 
indefinite integral operator from the Math palette or press and hold 
the {\b Ctrl }key and type " {\b  i  }".  Fill in the placeholders 
with the expressionto be integrated. }
.EQN 12 33 790 0 0
(({0:x}NAME,(1)/(1+{0:sin}NAME({0:x}NAME))){67})
.TXT 6 -33 501 0 0
Cg a76.125000,76.125000,127
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Select the 
complete expression and choose  {\b\ul E}{\b valuate} => {\b\ul S}{\b 
ymbolically} from the {\b\ul S}{\b ymbolics} menu. \par \par \pard 
Mathcad returns the answer:}
.EQN 10 24 502 0 0
(-{0}2)/(({0}1+{0:tan}NAME(({0}1)/({0}2)*{0:x}NAME)))
.TXT 7 -24 506 0 0
Cg a76.000000,76.000000,292
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b\ul \tab S}{\b implify}  
\par \par \pard \tab By using the keyword simplify, Mathcad can carry 
out the simplification of algebraic and trigonometric expressions.{\b  
\par \par }\pard {\b \tab }1.  Enter the expression to be simplified.  
Hint: use captial X rather than lower case to avoid having Mathcad 
plug in any previously used definintion of x.  {\b  }}
.EQN 16 25 509 0 0
(({0:X}NAME)^(2)-3*{0:X}NAME-4)/({0:X}NAME-4)+2*{0:X}NAME-5
.TXT 5 -25 508 0 0
Cg a76.375000,76.375000,304
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Press and hold 
the {\b Ctrl} and {\b Shift} keys and type  " {\b  . }  " key.   
Mathcad displays a placeholder to the left of the arrow.  Type "  {\b 
simplify  }"{\b  } into the placeholder and either click outside the 
math region or press the {\b Enter} key.\par \par Mathcad returns the 
simplified expression to the right of the arrow }
.EQN 10 22 800 0 0
{   45   271 0 0}{61}
19778 36776 0 0 44
40 271 45 1 24 0 36720 0 0 0 0
"s"<LVLVLVLV)@It!!>{5hLVLVLVLJ#d!Q!,!(<6LVLVLVJCLG)1"s"<LVLVLVLV)@It!".[5]A`"S!'LGAa*rIt!0LVLVKBLG)1$W"<.JIt!!DF!Q!`LG)1LVLVLOG,!Q!6!(:DLG)1"2It!$4&$'#dLVLV8^It!"9Q5^.Z"#!9LH&K#dIt!!<6!Q#dLVLV90It!".[5^6j!Q!]LG)1"2It!0LVLVKBLG)1$W"</LIw!$LV!Q!$LG)1LVLV
LOG,!Q!:!(:DLG)1"2It!$DF!Q!$LG)1LVLVLOG,!Q!6!(:ALG)1#4It!$DF"##dLVLV90It!"Iq5]A`"S!'LGAa*rIt!0LV*BIz!#>z"S!fLGAaCDIt!">{5hLVFJIt!$+t!Q!3LG)1(nIt!!DF!Q#+LG)1%Y"<LVL2LG)1*BIt!")0!Q!KLG)1#4It!-4&!Q!~!(<6LG)1%8J"!")0"S!'LGAa(nIz!"9P"S!'LH&K!`Iw!!+t"#!$LG)1
!`Iw!!4&%Y!-LG)1#dIw!!<6"#!$LG9Q!`Iz!!+t#U!WLG)1%8I}!"1@"S!'LGAa*rIw!(.[5hLV!Q!<LG)1"2It!"1@!Q!-LG)1+DIt!"1@!Q!'LG)1"2It!!4&!Q!'LG)1"2It!!4&"#!'LG)1"2It!!4&!Q!'LG)1#4It!!+t!Q!<LG)1!`It!!+t!Q!*LG)1"2It!%1@!Q!BLG)1$fIt!!DF!Q!`LG1A2s"<LVIt!"Ip!Q!?LG)1"2It
!%)0!Q!9LG1A"2It!!4&!Q!'LG)1"2It!!4&!Q!*LG)1"2It!!4&!Q!'LG)1#4It!!+t!Q!<LG)1"bIt!!<6!Q!*LG9Q+tIt!"Ip!Q!9LG)1"2It!$4&$'"@!(9ZLT>{$6J(!"9P!Q!*LG)1$6Iw!"9P$'!<LG)1$6Iw!!DF!Q!'LG)1"2It!!4&!Q!'LG)1"bIt!!4&!Q!'LG)1"2It!!<6!Q!'LG)1%hIt!!<6!Q!*LG)1"2It!!<6!Q!?
LI+u%hIt!!4&!Q!3LG1A%8J%!!LV!Q!*LG1A3U"<LVIt!#&J!Q!BLG)1,vIt!")0!Q!'LG)1!`Iw!!+t"S!$LG1A!`It!!+t"S!'LG)1"2It!!+t"#!'LG)1"bIt!!<6!Q!9LG)1"2Iz!!+t"#!'LG)1"bIt!$DF!Q!9LG1A&jIt!$DF!Q!'LG1A23"<LVIt!#.Z!Q!<LG1A,FIt!"9P"S!'LG)1"2It!!+t"#!$LG)1"bIt!!+t"#!*LG)1
"2It!!+t$W!$LG9Q$6Iz!!4&!Q!$LG)1!`It!!<6#U!WLG)1&:It!"Ip"#!`LG)1!`Iw!$9Q5hLV!Q!ELG)1%8It!!4&!Q!ZLG1A2"It!!LV!Q!QLG)12"It!#.Z!Q!9LG)1"2It!$DF!Q!$LG1A+%"<LVJ.LG)1"bIt!"1@!Q!-LG)1*rIt!'#d"#!0LG)1"2It!#6j!Q"ALG)1"bIt!"1@!Q!-LG)1+DIz!$4'5hLV&:Iz!"1@"S!'LGAa
)pIz!#.Z!Q!WLG)1"2It!!<6"S!`LG)13$Iz!"1@"S!'LGAa*rIw!##e5YLV"S!'LGAa+tI}!"1@"S!'LGAa*rIt!0LVLVJaLG)1&["<$6It!!DF!Q!rLG)1$fIt!!DF!Q!`LG)1LVLVLKIp!Q!B!(9fLG)1"2It!&.Z!Q!9LG)1"2It!$4&$'#dLVLV-xIt!#9Q5Z9P"#!KLH&K%hIt!!4&!Q!3LG1A%8J%!!LV!Q!*LG)1LVLVLKIp!Q!>
!(9lLG)1.zIw!#&J!Q!]LG)1"2It!0LVLVJaLG)1%y"<%8Iw!&.Z!Q!?LG1A+tIt!!+t!Q#dLVLV.JIt!#.[5Z1@!Q!'LG)1/LIt!"9P!Q!'LG)1+DIt!!+t!Q#dLVLV.JIt!#.[5Z)0!Q!-LG)1,vIt!!<6!Q!6LG)1#4It!$DF"##dLVLV.JIt!##e5YLV"S!'LH>{)pIz!"1@"S!'LGAa*rIt!0LVLVJaLG)1#u"<(nIt!!4&!Q#dLVLV
K$It!!DG5\#d!Q#dLVLVL&It!!DG5\+t!Q#dLVLVKTIt!!DG5\4&!Q#dLVLVK$It!!DG5\4&!Q#dLVLVK$It!!DG5\4&!Q#dLVLVK$It!"#e5[>z!Q!*LG)1LVLVLV4&!Q!.!(9~LG9QLVLVLV<6!Q!,!(<6LVLVLVJCLG)1"s"<LVLVLVLV)@It!!>{5hLVLVLVLJ#d!Q!,!(<6LVLVLVJCLG)1

.TXT 9 -22 511 0 0
Cg a76.250000,76.250000,119
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab \tab \tab A more 
direct method is to select the expression to be simplified and then 
choose {\b\ul S}{\b implify} from the {\b\ul S}{\b ymbolics} menu. }
.TXT 5 0 512 0 0
Cg a76.500000,76.500000,211
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard To simplify a 
trigonometric expression by having Mathcad apply the following two 
identities:\par \par \pard \tab \tab \tab \tab sin{\up 2}(x) + cos{\up 2}
(x) = 1    and   cosh{\up 2}(x) -sinh{\up 2}(x) = 1\par \pard \par 
\tab 1.  Enter the trigonometric expression to be simplified.\tab }
.EQN 13 7 792 0 0
{0:sin}NAME*(({0:ln}NAME({0:a}NAME*{0:b}NAME)))^(2)
.TXT 3 -7 804 0 0
Cg a76.375000,76.375000,239
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Press and hold 
the {\b Ctrl }and {\b Shift} keys and type  " {\b  . }  " key.   
Mathcad displays a placeholder to the left of the arrow.  Type "  {\b 
simplify, trig }{\b " } into the placeholder and either click outside 
the math region or press the {\b Enter} key.}
.EQN 5 8 127 0 0
{   25   269 0 0}{61}
19778 20256 0 0 44
40 269 25 1 24 0 20200 0 0 0 0
"s"<LVLVLVLV(>Ir!$.[5\LV!Q!KLG)1)pIt!!DF!Q!WLG)1*rIz!#>z"S!fLGIqFzIt!#>z!Q!TLG)1#4It!"Ip!1!^!(:/LG)1(>It!$<6!Q!-LG)1)@It!$LV!Q!TLG)1$6It!#G,!Q!-LG1AExIt!#>z!Q!ZLG)1#4It!"A`!1!b!(:,LG)1(>It!$LV!Q!-LG)1(>It!%)0!Q!WLG)1$6It!#>z!Q!-LG)1!`It!.)0!Q!KLG)1+tIt
!!DF!Q!9LG#e:C"<"bIz!!4&$'!$LGAa#4J%!!+t#%!3LGAa$6Iz!!DF!Q!-LG)1'<It!!LV"S!'LH&K!`Iw!!+t"#!$LG)1!`Iw!!4&%Y!-LG)1#dIw!!<6"#!$LG9Q!`Iz!!+t#U!*LG)1*rIt!"A`"S!ZLG1A#4Iz!!<6"S!'LG)1#4J%!!+t#%!3LGAa$6Iz!!DF!Q!-LG)1$fIr!/#e5Y<6!Q!'LG)1"2It!!4&!Q!*LG)1!`It!!LV
!Q!'LG)1"bIt!!+t!Q!0LG)1"2It!")0!Q!*LG)1"bIt!!DF!Q!ELG)1#dIt!!4&!Q!'LG)1"2It!!4&!Q!'LG)1"2Iw!!4&!Q!'LG)1"2It!!4&!Q!-LG)1!`It!"A`!Q!$LG)1!`It!!<6!Q!'LG)1$fIt!$DF!Q!<LG)1*rIt!!4&!Q!'LG)1"bIt!!4&!Q!'LG)1!`It!!LV!Q!'LG)1"bIt!!+t!Q!0LG)1"2It!")0!Q!*LG)1"bIt
!!DF!Q!6LG#eCu"<#dIw!!4&!Q!'LG)1"bIt!!+t!Q!0LG)1"2It!!<6!Q!$LG)1#dIt!!4&!Q!3LG)1"bIt!!<6!Q!-LG)1'<It!"1@"#!'LG)1"2It!!4&!Q!'LG)1"2It!!<6!Q!'LG)1"2It!!4&!Q!-LG)1!`It!"A`!Q!*LG)1"bIt!!<6"S!-LG)1+tIt!"9P!Q!ZLG)1#dIt!!<6!Q!-LG1A!`It!!LV!Q!'LG)1"bIt!!+t!Q!0
LG)1"2It!")0!Q!*LG)1"bIt!!DF!Q!6LG#eE9"<"bIw!!DF!Q!'LG)1"bIt!!+t!Q!0LG)1"2It!!<6!Q!$LG)1$6Iz!!4&!Q!*LG)1"bIt!!<6!Q!-LG)1'<It!!LV"#!-LG)1"2It!!4&!Q!'LG)1"2It!!<6!Q!'LG)1"2It!!4&!Q!*LG)1"2It!"A`!Q!*LG)1"bIt!!4&!Q!*LG)1"bIt!#&J'-!6LG)1$fJ%!")0!Q!0LG)1"bIt
!!4&"#!*LG)1#dIt!!4&!Q!*LG)1!`It!")0"S!'LG)1"bIt!!<6!Q!*LG)1#4It!"1@!1#F!(9ZLG)1"2It!!+t"#!$LG9Q"2It!!+t!Q!0LG)1!`Iz!!4&!Q!$LG)1#dIt!!4&!Q!3LG1A"2It!!<6!Q!-LG)1'<It!!LV!Q!'LG)1!`Iw!!+t"S!$LG1A!`It!!+t"S!'LG)1"2It!!+t"#!'LG)1"bIt!!<6!Q!9LG)1"2Iz!!+t"#!'
LG)1"bIt!!<6!Q!`LG)1%8It!$<6!Q!'LG)1"2It!!<6!Q!'LG)1"2It!!+t!Q!0LG)1!`Iz!!4&!Q!$LG)1#dIt!!4&!Q!3LG1A"2It!!<6!Q!-LG)1$fIr!-#e5YDF"S!'LG)1"2It!!+t"#!'LG)1#dIt!!4&!Q!$LG1A"2It!")0"#!6LG)1!`Iw!!DF!Q!-LG)1'<It!")0"S!'LG)1"2It!!+t"#!$LG)1"bIt!!+t"#!*LG)1"2It
!!+t$W!$LG9Q$6Iz!!4&!Q!$LG)1!`It!!<6#U!'LG)1+DIt!"A`!Q!]LG9Q"bIz!!DF"S!$LG)1#dIt!!4&!Q!$LG1A"2It!")0"#!6LG)1!`Iw!!DF!Q!-LG)1$fIr!&#e5\<6!Q!-LG)1%hIt!#>z!Q!3LG)1#4It!#>z!Q!xLG)1#dIt!$#d!Q!TLG)1+DIt!"Ip!Q"5LG)1#4It!"A`!Q!KLG)1$6It!!DF!Q!9LG#e.k"<+DIt!!4&
"#!?LG)1'<Iw!!LV!Q!-LG)1)@It!&&J"#!0LG)1"2It!#6j!Q!QLG)10~Iw!(1@!Q!'LG1A&:It!#.Z"#!0LG)1#4It!"A`!1!~!(9lLG)1&jIt!!4&!Q!BLG)1'<It!!DF!Q!-LG)1#dJ"!"9P!Q!9LG)1*BIt!!4&!Q!*LG9Q+tIt!"1@!Q"&LG)15XIt!!4&!Q!BLG)1'<It!!DF!Q!-LG)1#dJ#!".[5e4&!Q!'LG)1LVLVLKA`!Q!'
LG+u#u"<CDIt!0LVLVJgLG)1"2Ir!"#e5eDF!Q#dLVLV/LIt!!+t!1!.!(;dLG)1LVLVLL.Z!a!.!(;dLG)1LVLVLL.Z!a!.!(;dLG)1LVLVLL.Z!a!6!(;XLG)1"bIt!0LVLVJ[LG)1"bIu!"#e5e4&"S#dLVLV.JIz!!+t!1!,!(<6LVLVLVJ=LG#e"s"<LVLVLVLV(>Ir!!>{5hLVLVLVLI>z!1!,!(<6LVLVLVJ=LG#e

.TXT 9 -8 466 0 0
Cg a76.375000,76.375000,158
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b\ul \tab E}{\b xpand
\par \par }\pard To expand all powers and products of sums in an 
expression, the keyword {\b expand} is used.\par \pard \par \pard \tab 
1.  Enter the expression to be expanded\tab \tab \tab \tab \tab \tab 
\tab           \tab \tab \tab }
.EQN 14 23 458 0 0
((5-2*{0:X}NAME))^(-3)+(1)/(8)*(((2)/({0:x}NAME)+1))^(2)
.TXT 5 -23 459 0 0
Cg a76.500000,76.500000,297
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Press and hold 
the {\b Ctrl} and {\b Shift} keys and press the  " {\b  }.   " key.  
Mathcad displays a placeholder to the left of the arrow.  Type {\b expand} 
into the placeholder and either click outside the math region or press 
the {\b Enter} key.\par \pard \par \pard Mathcad returns the expanded 
expression to the right of the arrow }
.EQN 12 16 801 0 0
{   53   383 0 0}{61}
19778 61112 0 0 44
40 383 53 1 24 0 61056 0 0 0 0
#5"<LVLVLVLVLVK6LG)1$7"<LVLVLQ9P!Q">LG)1LVJjLG)1$7"<LVLVLQ1@!Q"DLG)1LVJgLG)1$7"<LVLVLQ)0!Q"JLG)1LVJdLG)1(_"<LVLVLPLV!Q!-LG9Q*BJ"!")0"S!'LGAa"2It!&.Z#U!0LG1A!`Iw!-DF!Q!V!(<6LVLV<6It!"1@!Q!WLG)1"2It!"1@!Q!-LG)1#4It!&6j!Q!'LG)1$6It!!+t!Q#4LG)1'}"<LVLVLPLV
!Q!9LG)1*BIt!"Ip!Q!'LG)1#dIt!&>z!Q!<LG)1DvIt!$#e5hLVLVKTLG)1%8It!!LV$'!9LG)1"bIt!")0"#!3LG)10~It!!<6!Q!-LG)1DvIt!#9Q5hLVLVKTLG)1%8It!$<6!Q!BLG)1$6It!&G,!Q!6LG)1!`It!-LV!Q!P!(<6LJDF!Q"&LG)1KTIt!"1@!Q!`LG)1%hIw!")0!Q"#LG)1#dIw!!+t"##1LG)1(?"<LVJLLG)13$It
!0<6!Q!-LG1A,FIt!"9P!Q!'LG)1#4It!'+t!Q#OLG)1)a"<LVJILG)14&It!0<6!Q!-LG)1*BIt!!<6!Q!6LG)1#4It!!4&!Q!{LG)1"bIt!/>z!Q!l!(<6LG<6"S!BLG)1$6Iw!!+t"#!uLG)1KTIt!!<6"S!TLG9Q$fIz!!4&#%!0LGAa,vIz!#&J#U!`LGIq#dIw!!+t"#!`LG9Q"bIt!%.[5hLV"2It!!<6!Q!?LG)1$fIt!!+t!Q!x
LG)1LVKKLG)14&It!!4&!Q!cLG)1"2It!")0!Q!$LG)1+tIt!!<6!Q!'LG)1*#"<LVIwLG)1"bIt!"A`!Q!<LG)10~It!0LV:2It!()0!Q!lLG)1%hIt!%)0!Q!*LG)1"2It!$9Q5hLV"bIt!!+t!Q!?LG)1%hIt!&G,!Q#dLP+t!Q"8LG)1-xIt!!<6!Q!-LG)1,vIt!!+t!Q!*LG)1*#"<LVI}LG)1&jIt!"9P!Q!$LG)10NIt!0LV90Iw
!(A`!Q!iLG)1$fIt!!+t!Q!fLG)1#4It!$DG5hLV"bIt!!+t!Q!<LG)1%8Iw!!+t"#!{LG)1LVKBLG)16*It!%A`!Q!0LG1A!`Iw!$LV!Q!$LG)1"bIt!#DG5hLV"2It!!<6!Q!9LG)17,It!0LV9`It!(9P!Q!lLG)10NIt!!<6!Q!'LG)1*c"<LVIwLG)1"bIt!"9P!Q"DLG)1LVK9LG)1"bIt!'DF!Q!*LG)1+tIt!!<6!Q!{LG)1"bIt
!!4&!Q!P!(9`LG)16*It!(9P"S!<LG)17,It!%1@"S#dLJ<6"S"5LG9Q,vIz!'#d"S!*LG)1%y"<#4It!)&J!Q"\LG)17,It!%9P!Q#dLVLV7,It!"DG5Y<6!Q"JLG)1:bIt!)&J!Q!iLG)1LVLVLO&J!Q"(!(9WLG)1#4Iz!$4&#U!3LG9Q"2I}!!4&!Q!lLG)1,vIt!%1@!Q!<LG9Q$fIt!#>z"#!'LG1A!`Iw!!+t!Q!$LG1A#4J(!!+t
"S!'LG1A!`It!$4&!Q#ILG)15XIt!'4&!Q!TLG)14w"<"2It!"1@!Q!WLG)1"2It!"1@!Q!-LG)1#4It!%A`!Q!fLG)1,vIt!"Ip!Q!9LG)1'lIt!!4&!Q!'LG)1!`It!!4&"#!'LG)1"2It!!4&!Q!'LG)1"bIt!!4&!Q!'LG9Q*BIt!/&J!Q";LG)12RIt!$+t!Q",!(9WLG)1%8It!$4&!Q!?LG)1"2It!!LV!Q!lLG)1,vIt!%1@!Q!?
LG)1%8It!#6j!Q!3LG)1"bIt!!<6!Q!'LG)1"2It!!4&!Q!*LG)1"2It!!<6!Q!]LG)1FzIt!(9P!Q")LG)1)pIt!).[5Y4&!Q!9LG)1#dJ%!"9P!Q!*LG)1$6Iw!")0!Q!cLH.[$6J(!!<6!Q!*LG)1$fJ(!")0$W!6LG)1%8It!#6j#%!*LG)1"bIt!!<6!Q!*LG9Q"2It!!<6!Q!'LG)1"bIt!"Ip'-!3LQG-$6J(!")0,7!3LH.[$6JC
!")0$W!3LH.[!`It!'DG5Y4&!Q!9LG)1*rIt!#&J!Q!3LG)1-xIt!%1@!Q!fLG)1&:It!"9P!Q!HLG)1"2It!!4&!Q!$LG)1!`Iz!!4&!Q!'LG)1"2It!!+t"S!'LG)1"2It!!4&"#!]LG)1FzIt!(9P!Q")LG)1)pIt!'.[5Y4&!Q!6LG)1+tIt!"A`"#!3LG)1-xIt!%1@!Q!fLG)1&:It!"9P!Q!KLG1A"2Iw!!+t"#!$LG)1!`Iw!!DF
"#!*LG)1!`Iw!!DF"#!$LG)1*rIt!/&J!Q";LG)12RIt!$+t!Q!f!(9ZLG)1#4Iw!%)0!Q!9LG)1"2It!!DF!Q!oLG)1,vIt!%1@!Q!?LG)1%8It!*#d!Q!WLG)1G|It!(9P!Q")LG)1)pIt!$.[5YDF!Q!-LG)1*BIt!!<6!Q!6LG)1#4It!!4&!Q"\LG)12"Iw!"9P!Q"PLG1ALVLVLJ<6!Q!R!(9`LG)1"bIz!$+t"S!6LG9Q"2I}!#G,
#%"&LG)12RIt!"9P!Q"SLG)1LVLVLJ<6!Q!L!(;^LG)1+DIz!"A`!Q!9LGIq0NIt!0LV*rIz!+9P"S",LG9Q/LIz!!<6!Q!P!(;^LG)1+tIt!"Ip!Q!<LG)1"2It!&>z!Q#dLJDF!Q"qLG)14&It!&>z!Q!-LG)1)!"<<6J%!"9P!Q!`LG)1&:It!"Ip!Q"#LG)1LVJOLG)1>jIt!'LV!Q!{LG)1#4It!#>{5e+t"#!cLG)1&:It!#&J!Q!~
LG)1LVJOLG)1>jIt!'LV!Q!{LG)1#4It!#>{5e4&!Q!cLG)1&jIt!"Ip!Q!{LG)1LVJRLG)1>jIt!'LV!Q!{LG)1#4It!#>{5e<6!Q!`LG)1&jIt!#&J!Q!xLG)1LVJRLG)1>jIt!'LV!Q!{LG)1#4It!#Iq5dG,!Q!*LG)1+tIt!#&J!Q!BLG)1/|It!0LV+tIt!+Ip!Q"2LG)10NIt!!DF!Q!P!(;ULG9Q+tIw!#.Z!Q!3LG)1"bIt!&.Z
!Q#dLJLV"#"nLG1A3TIw!&6j"#!-LG)1(_"<LVI}LG)1'<It!"1@"S!xLG)1#4J"!0LV'lIt!+Ip!Q"2LG)10NIt!!DF!Q!<!(<6LJ4&!Q"2LG)1$6It!!4&!Q#dLVLV@>It!"4'5hLV*rIt!'<6!Q!9LG)1LVLVLRG,!Q!8!(<6LJDF!Q"&LG)1&:It!0LVLVKoLG)1#U"<LVK{LG)1LVLVLR6j!Q!0!(<6LS4&!Q#dLVLV@>It!!Iq5hLV
BrIt!0LVLVKlLG)1$7"<LVKoLG)1"bIt!0LVLVKlLG)1#U"<LVKrLG9QLVLVLR>z!Q!.!(<6LVLVLVLVLO&J!Q!.!(<6LVLVLVLVLO&J!Q!.!(<6LVLVLVLVLO&J!Q!.!(<6LVLVLVLVLO&J!Q!Q

.TXT 10 -16 461 0 0
Cg a76.500000,76.500000,117
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab \tab \tab A more 
direct method is to select the expression to be simplified and then 
choose {\b Expand} from the {\b\ul S}{\b ymbolics} menu. }
.TXT 9 -1 462 0 0
Cg a78.000000,78.000000,138
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b\ul \tab F}{\b actor }
\par \par To factor an expression using Mathcad, the keyword {\b factor} 
is used.\par \par \tab 1.  Enter the expression to be factored\tab 
\tab \tab \tab \tab \tab \tab           \tab \tab \tab }
.TXT 17 1 523 0 0
Cg a76.500000,76.500000,413
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Press and hold 
the {\b Ctrl} and {\b Shift} keys and press the  " {\b  .}   " key.  
Mathcad displays a placeholder to the left of the arrow.  Type {\b 
factor, }then the "{\b square root sign}"  from the Arithmetic palette 
and then  {\b 2}   into the placeholder and then either click outside 
the math region or press the {\b Enter} key.\par \pard \par \pard 
Mathcad returns the expression factored with respect to the square 
root of two to the right of the arrow }
.EQN 16 15 805 0 0
{   25   240 0 0}{61}
19778 18056 0 0 44
40 240 25 1 24 0 18000 0 0 0 0
#U"<L&It!/>z!Q"zLG)1(>J2!(<3LG)18^It!&G,!Q!?LG)1&jIt!()0!Q!?LG)1"bJ6!(;yLG)1$6Iw!)6j!Q!~LG1A&:It!"Ip!Q"5LG1A&:It!!<6)!"<HNIt!!LV!Q!$LG)17\It!&G,!Q!$LG)1&:It!"A`!Q"5LG)1!`It!"Ip!Q!'LN>{5Y<6"S!'LGAa+tJ"!!LV"S!*LGAa"2Iw!!<6"#!*LG9Q"2Iz!!<6"#!-LG)1"2It!!<6
#U!WLG)1)pIt!!<6"S!'LGAa$fIt!"Ip!Q!'LG)1"bJ"!!4&!Q!<LG)1&:Iz!!4&#%!6LG)1&:It!!4&!Q!*LGIq"2It!!4&:c"<#4It!!DF!Q!iLG)1"2It!")0!Q!*LG)1"2It!!4&!Q!'LG)1"2It!!+t!Q!$LG)1"bIt!!4&!Q!?LG)1"2It!!DF!Q!'LG)1*rIt!#G,!Q!0LG)1#4It!"A`!Q!?LG)1"2It!!DF!Q!'LG)1"bIt!"1@
!Q!ELG)1#4It!"A`!Q!?LG)1"2It!!DF!Q!'LG)1"bIt!!+t6["<#dIt!!4&!Q!oLG)1%8It!!<6!Q!'LG)1"2It!!LV!Q!*LG)1"bIt!!4&!Q!<LG)1"bIt!!LV!Q!cLG)1(>It!")0!Q!'LG)1&:It!"A`!Q!*LG)1#dIt!!LV!Q!6LG)1'lIt!!4&!Q!?LG)1%hIt!!<6!Q!0LG)1#dIt!!+t6["<$6Iw!#>z$'!9LG)1$fIt!!DF"S!'
LG)1#dIt!!<6!Q!*LG)1"2It!"9P"#!*LG)1$6It!#&J'-!0LH&K"2It!"1@"#!9LH.[#dIw!!<6!Q!3LG)1#4It!!<6!Q!*LG)1"bJ%!!LV"#!9LH.[#dIw!!<6!Q!3LG)1#4It!!+t35"<$fIt!&.Z!Q!6LG)1"bIt!!4&!Q!'LG)1"2It!!4&!Q!*LG)1"bIt!!+t"S!HLG)1#dIt!$LV!Q!KLG)1%8It!#&J!Q!KLG)1#dIt!!DF!Q!6
LG)1(nIt!#&J!Q!KLG)1#dIt!!DF!Q!$LM)15Z)0"#!xLG)1#dI}!!4&"#!-LG9Q!`Iz!!<6"S!*LG)1!`It!#.Z!Q!3LG)1*rIt!#G,!Q!6LG1A&jIt!#>z!Q!3LG)1"bIt!"1@!Q!KLG1A&jIt!#>z!Q!3LG)1"bIt!!+t0O"<#dIt!!4&!Q!uLG)1$6It!#G,!Q!lLG)1$6It!$4&!Q!QLG)1$6It!!4&!Q!?LG)1(>It!")0!Q!*LG)1
$fIt!#6j!Q!'LG)1&:It!#>z!Q!3LG)1"bIt!!+t1q"<#4It!!DF!Q!fLG)1"bIt!")0!Q!'LG)1'<It!%A`!Q!'LG)1"bIt!'<6!Q!0LG)1#4It!%9P!Q!'LG)1"bIt!!<6!Q!6LG)1'<It!!DF!Q!iLG)1"2It!!<6!Q!*LG)1!`J^!(9ZLG9Q"2J.!$+t"S!9LG9Q4VIt!!<6"S"/LG)1#4Iz!!4&#%!cLG)1"bIz!!DF!Q!6LG)1&jIz
!!4&#%!cLG)1"bIz!!DF!Q!$LI4'5[6j!Q!'LG)1DvIt!(A`!Q"/LG)1%hIt!"1@!Q"DLG)1%hIt!!+t&{"<(>It!.9P!Q"ALG)13$It!"9P!Q!<LG)16ZIt!"9P!Q!'LI)15[G,!Q#:LH.[3TIt!'<6$W!'LG)1%hIt!(Ip$W!'LG)1"2J,!(:#LG)1LVJgLG)17,It!"Ip!Q"YLG)1"bJ,!(:#LG)1LVJjLG)16ZIt!#&J!Q"VLG)1"bI|
!(:#LG)1LVLVLPLV#U"<'<It!!<6!Q#dLVLV<6I|!(9xLG9QLVLVLQ)0"3"<LVLVLT)0"3"<LVLVLT)0"3"<LVLVLT)0"3"<LVLVLT)0

.TXT 23 -15 518 0 0
Cg a76.500000,76.500000,153
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b \tab }{\b\ul C}{\b 
ollect }\par \par \pard \tab To simplify an expression by collecting 
terms containing like powers of a variable, the keyword {\b collect} 
is used.\par \par \tab 1.  Enter the expression.\tab }
.EQN 14 23 519 0 0
({0:X}NAME)^(2)-{0:a}NAME*{0:Y}NAME*({0:X}NAME)^(2)+2*({0:Y}NAME)^(2)*{0:X}NAME-{0:X}NAME
.TXT 5 -23 520 0 0
Cg a76.500000,76.500000,333
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab 2.  Press and hold 
the {\b Ctrl} and {\b Shift} keys and press the  " {\b  .}   " key.  
Mathcad displays a placeholder to the left of the arrow.  Type {\b collect}{
\b ,X}  into the placeholder and theneither click outside the math 
region or press the {\b Enter} key.\par \par \pard Mathcad returns the 
expression with the like powers of  X collected to the right of the 
arrow }
.EQN 15 11 130 0 0
{   25   388 0 0}{61}
19778 29156 0 0 44
40 388 25 1 24 0 29100 0 0 0 0
"s"<LVLVLVLVLVKELH#e5hLVLVK{LG)15XIt!0LV-xJ*!(<6LVLV,vIt!(A`!Q"ALG)17,It!-+t%Y"<LVLVLK9P!Q"8LG)17\It!(A`!Q"SLG)1)pKN!(9ZLG9Q"2I}!%1@#%!3LG9Q%hIz!!4&#%!HLG)1%8J"!"1@"S!NLG9Q"2I}!$#d"S!'LGAa$6Iw!!DF"S!'LH&K"2Iw!!DF"#!*LG1A"bIw!!<6"S!'LGAa)pIt!"9P!Q!0LG9Q
*rI}!")0"S!3LG)1$fIz!!4&#%!HLG)1&:It!!4&#U!6LG9Q.JIz!!<6!Q!9LG9Q"2Iz!,Iq5YDF!Q!-LG)1-HIt!!4&!Q!9LG)1&jIt!!DF!Q!NLG)1%hIt!!4&!Q!9LG)1)pIt!!DF!Q!ZLG)1#4It!"1@!Q!'LG)1"2It!!<6!Q!'LG)1"2It!!4&!Q!'LG)1"2It!!4&!Q!'LG)1!`It!"9P!Q!-LG)1+DIt!"1@!Q!3LG)1*rIt!!4&
!Q!9LG)1$fIt!"9P!Q!-LG)1(nIt!"Ip!Q!*LG)1"2It!"9P!Q!uLG)1#4It!"A`!Q!-LG)1!`K\!(9`LG)1"2It!%A`!Q!'LG)1%8It!#.Z!Q!'LG)1)@It!"Ip!Q!?LG)1*BIt!!4&!Q!`LG)1"2It!"9P!Q!0LG)1"bIt!!4&!Q!'LG)1"2It!!LV!Q!0LG)1&jIt!!4&!Q!cLG)1$6It!")0!Q!ZLG)1"2It!"9P!Q!6LG)1%hIt!!4&
!Q!QLG)1&:It!!DF!Q!?LG)1/LIt!!DF!Q!?LG)1"2It!!4&?M"<$6Iw!#>z$'!6LG9Q"2It!!LV!Q!3LG)1$6Iw!#>z$W!9LG)1"bIt!!LV!Q!ELG)1$6Iw!"9P$'!<LG1A%hIt!!LV!Q!*LG)1"2It!!4&!Q!'LGAa"2It!!LV!Q!ELG1A'lJ7!!LV!Q!3LG)1$fJ%!"1@"S!'LG)1#dIt!"1@!Q!*LG)1$6Iw!#>z$W!3LG)1$6It!!<6
!Q!0LG)1(nJ%!"1@!Q!-LG)1#4It!")0"#!*LQ4'5Z1@!Q!oLG)1"2It!"1@!Q!$LG)1'lIt!$+t!Q!BLG)1%8It!!+t!Q!ZLG)1-HIt!"A`!Q!'LG)1"2It!!<6!Q!'LG)1"2It!!4&!Q!'LG)1"2It!!4&!Q!'LG)1'lIt!%1@!Q!3LG)1$6It!$<6!Q!'LG)1$fIt!!+t!Q!3LG)1&jIt!$+t!Q!<LG)1$6It!"9P!Q!$LG)1.zIt!!LV
!Q!BLG)1"bKD!(9cLG1A.zIw!"9P!Q!$LG)1'<Iw!$+t!Q!ELG)1$fIt!!+t!Q!WLG1A,vIw!"Ip"S!*LG9Q"bIt!!4&!Q!*LG1A#4Iz!!+t"S!BLG1A,FIt!"1@!Q!3LG)1+DIw!"9P!Q!$LG)1$6It!"Ip"#!TLG)1%hIt!"1@!Q!6LG)1!`It!&&J!Q!0LG)1&:Iw!!<6:#"<#dIt!!4&!Q"/LG)1"2It!"Ip!Q!'LG)1)@It!#.Z!Q!6
LG)1"2It!$#d!Q!'LG)1+tIt!!4&!Q!`LG)1"2It!#>z!Q!BLG)1"2It!$DF!Q!<LG)1#dIt!&>z!Q!'LG)1#4It!"Ip!Q!'LG)1)@It!"A`!Q!6LG)1$fIt!!4&!Q!oLG)1#dIt!"A`!Q!'LG)1"2KD!(9]LG)1#4It!'4&!Q!-LG)1%8It!!DF!Q!iLG)1"bIt!")0!Q!-LG)1(>It!!DF!Q!ZLG)1#4It!$<6"#!$LG1A(>It!"Ip!Q!-
LG)10NIt!!<6"#!xLG)1#4It!!4&!Q!?LG)1#4It!%A`!Q!*LG)1"bIt!")0!Q!-LG)1-HIw!!LV!Q!9LG)1#4It!!+t7]"<"bIz!!4&%Y!oLG9Q"2Iz!")0"S!'LH>{*BIz!")0"S!'LG9Q!`J"!")0"S!'LGAa)@Iz!!4&#%!WLG)1"2It!%9P"S!'LGAa/|It!!<6!Q!uLG9Q"2I}!"Ip"S!'LH>{*BIt!!DF"S!3LG9Q"2Iz!!+t#U!W
LG)1#dIt!"1@"S!'LG9Q*C"<'lIt!!4&!Q"YLG)1"2It!'LV!Q!'LG)1LVLVLJ#d!Q!'LG)1*BIt!%1@!Q!'LG)1-HIt!#G,&{"<(>It!*LV!Q";LG)1LVLVLJ<6!Q!]LG)1-HIt!%Ip!Q!NLI)15[G,!Q"bLG)15XIt!0LVLVJLLG)1*rIt!%A`!Q!lLG)1(nJ6!(:#LG)1<6It!(9P!Q#dLVLV*rIt!$4&!Q!oLG)1-HIt!#G,&{"<)@It
!*LV!Q";LG)1LVLVLJ<6!Q!WLG)1.JIt!%9P!Q!NLI)15\#d!Q"bLG)15XIt!0LVLVJLLG)1*BIt!%Ip!Q!iLG)1(nJJ!(9uLG)1"bIt!*+t!Q!*LG)13TIt!!<6!Q#dLVLV(nIt!!<6!Q!WLG)1,FIt!!<6!Q!fLG)1)@J6!(9xLG9Q;4Iz!()0"S#dLVLV)pIz!$DF!Q!cLG9Q-HIt!$#d#u"<LVLVLVLVBrIt!*+t!Q!QLH#e5hLVLVLV
LS4&!Q"VLG)1)@J$!(<6LVLVLVK{LG1A90It!$+t"s"<LVLVLVLVLVKELJ!Q

.TXT 6 -11 522 0 0
Cg a77.000000,77.000000,147
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab An alternate method 
for collecting terms of an expression is to click on a variable in the 
expression and choose {\b\ul C}{\b ollect} from the {\b\ul S}{\b ymbolics} 
menu. }
.TXT 6 0 797 0 0
Cg a76.625000,76.625000,4258
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Finding the 
solutions to equations:\par \par }\pard \tab To solve a single 
equation in a single unknown,the {\i root} function can be used.  This 
Mathcad function uses an expression and one of the variables from the 
expression.  It varies the variable until the expression is equal to 
zero.  It then returns the value that makes the expression equal zero.  
The root function has the form:\par \par \pard \tab \tab \tab \tab 
root ( f(z) , z )\tab \tab where f(z) is the function, and the value 
of z which makes the function equal to zero is returned as the 
solution.  The function can be a function which is defined elsewhere 
in the worksheet or an expression.\par \pard \par \pard \tab \tab To 
find the solution to the equation  \tab \tab  {\b x }{\b\up 3}{\b  - e }{
\b\up x} \par \pard \par \pard \tab 1.  First define a guess for the 
value of the variable.  This guess value must be placed before the 
root function in the Mathcad worksheet.  Define the guess value of  {
\b x} as 3: \par \pard \tab \tab \tab \tab \tab \tab \tab \tab \par 
\tab \tab \tab \tab \tab \tab \tab \tab {\object{\*\objclass \eqn}
\rsltpict{\*\objdata 
.EQN 512 56 7 0 0
{0:x}NAME:3
}} \par \pard \tab \tab \tab \tab \tab \par \pard \tab 2.  Arrange the 
function in a form that is equal to zero.  Select a variable name for 
the scalar which will be used to define the root of the equation.  
Using the variable {\b a} for this:\par \pard \par \tab \tab \tab \tab 
\tab \tab \tab \tab \tab \tab \tab \tab {\object{\*\objclass \eqn}
\rsltpict{\*\objdata 
.EQN 525 7 9 0 0
{0:a}NAME:{0:root}NAME(({0:x}NAME)^(3)-({0:e}NAME)^({0:x}NAME),{0:x}NAME)
}}\tab \par \par \pard \tab 3.  To have Mathcad show the root of the 
equation simply type {\b a=\par }\pard {\b \par }\pard {\b            }
Mathcad returns the answer:\par \pard \tab \tab \tab \tab \tab \tab 
\tab \tab \tab \tab \tab \tab {\object{\*\objclass \eqn}\rsltpict{
\*\objdata 
.EQN 537 7 10 0 0
{0:a}NAME={0}?_n_u_l_l_
}}\tab \tab \par \tab \tab \tab \tab \par \par \pard \tab 4.  If the 
equation has more than one root, the guess value will determine the 
root which is closest to the guess value. An alternate way to find 
multiple roots is to use the {\i polyroot} function.\par \pard \par 
\pard \tab The polyroot function does not require a guess value.  
However, it returns all of the roots of an equation at once, whether 
they are real or complex.   In order to use the polyroot function, the 
equation must be expressed as a vector.  This will not be covered in 
this material.\par \pard \par {\b Systems of equations:\par }{\b \par }
\tab Mathcad allows you to solve a system of up to fifty simultaneous 
equations in fifty unknowns.\par \par \pard \tab There are four steps 
to solving a system of simultaneous equations.  These are:\par \pard 
\par \pard \tab 1.  Provide an initial guess for all of the unknowns 
that are desired.  The initial guesses give Mathcad a place to start 
searching for solutions.\par \pard \par \tab \tab \tab \tab \tab \tab 
\tab \tab \tab {\object{\*\objclass \eqn}\rsltpict{\*\objdata 
.EQN 575 63 12 0 0
{0:x}NAME:1
}}\par \par \tab \tab \tab \tab \tab \tab \tab \tab \tab {\object{
\*\objclass \eqn}\rsltpict{\*\objdata 
.EQN 579 63 47 0 0
{0:y}NAME:1
}}\par \par \pard \tab 2.  Type the word {\b Given}.  This tells 
Mathcad that what follows is a system of equations.  It can be typed 
in any combination of upper and lower case letters and in any font.   
Be sure that it is not typed in a text region or paragraph\par \pard 
\par \tab \tab \tab \tab \tab \tab \tab \tab \tab {\object{\*\objclass 
\eqn}\rsltpict{\*\objdata 
.EQN 591 63 37 0 0
{0:Given}NAME
}}\par \par \pard \tab 3.  Type the equations and inequalities in any 
order below the word {\b Given}.  Make sure to use the symbol "=" to 
separate the left and right sides of each equation.  To get the 
correct  = sign, press and hold the {\b Ctrl} key and then press the {
\b =} key.  The left and right sides of an inequality can be seperated 
with any of the symbols <, >, {\ul <}, or {\ul >.\par }\pard {\ul \par 
\tab \tab \tab \tab \tab \tab \tab \tab }{\object{\*\objclass \eqn}
\rsltpict{\*\objdata 
.EQN 606 56 38 0 0
({0:x}NAME)^(2)+({0:y}NAME)^(2)÷6
}}{\ul \par \par }{\ul \tab \tab \tab \tab \tab \tab \tab \tab }{
\object{\*\objclass \eqn}\rsltpict{\*\objdata 
.EQN 610 56 40 0 0
{0:x}NAME+{0:y}NAME÷2
}}{\ul \par }\pard {\ul \tab }4.  Type an equation that invloves the {
\b Find} function.  It can be in any combination of upper and lower 
case letters in any font, size or style. \par \pard \par \pard \tab 
\tab \tab \tab \tab \tab \tab \tab {\object{\*\objclass \eqn}\rsltpict{
\*\objdata 
.EQN 620 56 42 0 0
{0:Find}NAME({0:x}NAME,{0:y}NAME)={0}?_n_u_l_l_
}}\par \pard \par \tab \tab \par \tab The answer is expressed as a 
vector.\par \par \tab If {\b Find} has one argument, it returns the 
value of that variable that solves the equation between it and the {\b Given}
.\par \par \tab If {\b Find} has more than one argument, it returns a 
vector of answers.\par \par \par \par \pard \tab Mathcad is very 
specific about the types of expressions that  can appear between the 
Given and the {\b Find}.  The table below lists all the expressions 
that can be placed in a solve block between these two functions.  
These expressions are often called constraints.  In the table below,  
x  and  y  represent real-valued scalar expressions,  z  and  w  
represent arbitrary scalar expressio\pard n.\par \par \tab Condition
\tab \tab \tab \tab Keystroke\tab \tab \tab Description\par \pard \par 
\tab z=w\tab \tab \tab \tab [Ctrl]=\tab \tab \tab Constrained to be 
equal\par \par \tab x>y\tab \tab \tab \tab >\tab \tab \tab Greater 
than\par \par \tab x<y\tab \tab \tab \tab <\tab \tab \tab Less than
\par \par \tab x{\ul >}y\tab \tab \tab \tab [Ctrl]0\tab \tab \tab 
Greater than or equal to\par \par \tab x{\ul <}y\tab \tab \tab \tab 
[Ctrl]9\tab \tab \tab Less than or equal to\par \par \par \tab Mathcad 
does not allow contraints with the equals sign with a slash through it 
to indicate not equal to, range variable or expressions involving 
range variables of any kind, and inequalities of the form a<b<c\par 
\par \pard \tab Solve blocks cannot be nested inside each other.  
Therefore, each solve block can have only one Given and one Find.  a 
function like f( x ) :=Find( x ) cna be defined at the end of one 
solve block and the same function used in another solve block.\par 
\par \tab Never use assignment statements such as initial guesses ( {
\b x := 1} ) inside a solve block.  Mathcad marks them with an 
appropriate error message.\tab }
.TXT 278 13 728 0 0
Cg a37.750000,37.750000,32
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\fs28\b EG31 MATHCAD 
EXERCISES\par SESSION 2}}
.TXT 9 -13 729 0 0
Cg a77.000000,77.000000,82
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Exercise 1:  Taking 
a Derivative\par }\par \tab a.  Find the first derivative of the expression}
.EQN 8 24 730 0 0
{0:x}NAME"2*({0:x}NAME)^(4)+3*({0:x}NAME)^(3)-({0:x}NAME)^(2)+2*{0:x}NAME
.EQN 3 80 761 0 0
{0}8+{0}3*({0:x}NAME)^({0}3)-({0:x}NAME)^({0}2)+{0}2*{0:x}NAME
.TXT 2 -98 808 0 0
Cg a65.000000,65.000000,109
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard b.  Find the second 
derivative of the same expression.\par \par \pard c.  Find the third 
derivative of the same expression.}
.TXT 8 -6 733 0 0
Cg a76.625000,76.625000,88
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Exercise 2:  Integrating}
\par \par \tab  a.  Find the indefinite integral of the following expression}
.EQN 6 96 762 0 0
({0}1)/({0}4)*({0:x}NAME)^({0}4)+({0}2)/({0}3)*({0:x}NAME)^({0}3)
.EQN 2 -71 735 0 0
({0:x}NAME)^(3)+2*({0:x}NAME)^(2)
.EQN 0 81 763 0 0
(({0:x}NAME,({0:x}NAME)^(3)+2*({0:x}NAME)^(2)){67})
.TXT 4 -106 737 0 0
Cg a77.000000,77.000000,176
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard \tab   b.  Find the 
definite integral for the same expression between  {\b 0} and  {\b 5
\par \tab \par \tab }c.  Find the definite integral for the same 
expression between the symbolic limits of  {\b a}  to  {\b c } }
.EQN 3 97 764 0 0
({0}2875)/({0}12)
.EQN 2 10 765 0 0
(0&5`({0:x}NAME)^(3)+2*({0:x}NAME)^(2)&{0:x}NAME)
.TXT 3 -107 740 0 0
Cg a78.000000,78.000000,61
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Exercise 3:  Expanding}
\par \par \tab \tab \tab \tab  Expand the following expressions}
.TXT 7 21 741 0 0
Cg a57.000000,57.000000,3
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard a. }
.EQN 0 4 742 0 0
(({0:x}NAME+{0:y}NAME))^(4)
.EQN 0 82 766 0 0
({0:a}NAME&{0:c}NAME`({0:x}NAME)^(3)+2*({0:x}NAME)^(2)&{0:x}NAME)
.EQN 0 14 767 0 0
({0}1)/({0}4)*({0:c}NAME)^({0}4)+({0}2)/({0}3)*({0:c}NAME)^({0}3)-({0}1)/({0}4)*({0:a}NAME)^({0}4)-({0}2)/({0}3)*({0:a}NAME)^({0}3)
.TXT 3 -100 745 0 0
Cg a78.000000,78.000000,4
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard b.  }
.EQN 0 4 746 0 0
{0:cos}NAME(5*{0:x}NAME)
.TXT 4 -25 747 0 0
Cg a78.000000,78.000000,59
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Exercise 4:  Factoring}
\par \par \tab \tab \tab \tab Factor the following expression}
.EQN 2 52 799 0 0
(1)/({0:x}NAME-1)+({0:x}NAME)/({0:x}NAME+3)-2*({0:x}NAME)/({0:x}NAME+2)
.EQN 0 57 768 0 0
(({0:x}NAME+{0:y}NAME))^(4)
.EQN 1 10 769 0 0
({0:x}NAME)^({0}4)+{0}4*({0:x}NAME)^({0}3)*{0:y}NAME+{0}6*({0:x}NAME)^({0}2)*({0:y}NAME)^({0}2)+{0}4*{0:x}NAME*({0:y}NAME)^({0}3)+({0:y}NAME)^({0}4)
.EQN 4 -13 770 0 0
{0:cos}NAME(5*{0:x}NAME)
.TXT 1 -106 810 0 0
Cg a78.000000,78.000000,164
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Exercise 5:  Collecting}
\par \par In the following expression:\par \par \tab \tab \tab \tab 
\par \par \tab \tab \tab \tab a.   First collect  {\b x}  \par \par 
\tab \tab \tab \tab b.  Then collect  {\b y}\par \tab \tab \tab \tab 
\tab \par \tab \tab \tab \tab c.  Collect  {\b x}  and  {\b y}  at the 
same time}
.EQN 0 117 771 0 0
{0}16*({0:cos}NAME({0:x}NAME))^({0}5)-{0}20*({0:cos}NAME({0:x}NAME))^({0}3)+{0}5*{0:cos}NAME({0:x}NAME)
.EQN 7 -21 772 0 0
(-({0}2*({0:x}NAME)^({0}2)-{0}9*{0:x}NAME-{0}6+({0:x}NAME)^({0}3)))/((({0:x}NAME-{0}1)*({0:x}NAME+{0}3)*({0:x}NAME+{0}2)))
.EQN 1 -73 811 0 0
({0:x}NAME)^(2)-({0:ayx}NAME)^(2)+({0:by}NAME)^(2)*{0:x}NAME-{0:axy}NAME
.EQN 1 107 777 0 0
(1)/({0:x}NAME-1)+({0:x}NAME)/({0:x}NAME+3)-2*({0:x}NAME)/({0:x}NAME+2)
.TXT 10 2 788 0 0
Cg a78.000000,78.000000,33
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard This is not functioning 
correctly}
.EQN 1 -41 131 0 0
{   25   202 0 0}{61}
19778 15256 0 0 44
40 202 25 1 24 0 15200 0 0 0 0
"S"<LVLVLM#d!A!@!(:eLG&K!@Is!!&J!A"KLG&K!@Is!!&J!A#dLL1@!A!2!(:kLG&K9@Is!0&J!A"$LG&K#u"<6*Is!)Ip!A#VLG&K10Is!..[5Y4&!A!"LG&K!pIs!!&J!A!gLG&K!@Is!!&J!A!"LG&K$vIs!"4&!A!"LG&K!pIs!!&J!A!ILG&K%HIs!!&J!A!"LG&K!@Is!!&J!A!:LG&K'|Is!!&J!A!%LG&K!@Is!#Ip!A!"LG&K
!pIs!!&J!A!4LG&K!@Is!!G,!A!"LG&K!@Is!!6j!A!"LG&K!@Is!!&J!A!"LG&K!@Is!!6j!A!"LG&K#DIs!!&J!A!+LG&K!@Is!!>z!A!"LG&K"BIs!!&J!A!%LG&K!@Is!#A`!A!=LG&K7]"<"bIs!!.Z!A!gLG&K"BIs!"4&!A!%LG&K$vIs!!.Z!A!LLG&K%xIs!!6j!A!7LG&K!pIs!#9P!A!%LG&K*"Is!!.Z!A!4LG&K"BIs!!6j
!A!+LG&K"BIs!!6j!A!(LG&K"BIs!!6j!A!(LG&K"BIs!!.Z!A!7LG&K!pIs!$&J!A!:LG&K0o"<#4Is!%<6!A!(LG&K$vIs!!.Z!A!:LG&K(~Is!"LV!A!=LG&K!pIs!#A`!A![LG&K$vIs!"#d!A!+LG&K"BIs!!6j!A!(LG&K#tIs!"#d!A!@LG&K*RIs!"4&!A#V!(9]LG&K'LIs!!&J!A!"LG&K!@Is!!&J!A!"LG&K$vIs!!&J!A!"
LG&K"BIs!!>z!A!(LG&K"rIs!!G,!A!FLG&K!@Is!!&J!A!"LG&K!@Is!!&J!A!"LG&K%HIs!!>z!A!+LG&K"BIs!"DF!A!.LG&K$FIs!!&J!A!"LG&K!@Is!!&J!A!"LG&K$vIs!"4&!A!1LG&K"rIs!!6j!A!(LG&K"BIs!!&J!A!"LG&K!@Is!!6j!A!1LG&K&JIs!"<6!A!"LG&K!@Is!!&J!A!"LG&K!@Is!!&J!A!"LG&K!@Is!!&J
!A!"LG&K!@Is!"+t!A"@!(9ZLG&K!pIs!%4&!A!(LG&K$FIs!!>z!A!4LG&K!pIs!#A`!A!CLG&K$vIs!!>z!A!FLG&K!pIs!$.Z!A!%LG&K$FIs!!6j!A!(LG&K"rIs!!6j!A!(LG&K"BIs!!6j!A!(LG&K"BIs!!6j!A!=LG&K!pIs!$.Z!A!7LG&KEy"<"2Is!!&J!A!%LG&K!@Is!%4&!A!"LG&K$FIs!!&J!A!"LG&K!pIs!!&J!A!"
LG&K#DIs!!&J!A!%LG&K!@Is!#9P!A!FLG&K#tIs!!&J!A!"LG&K!pIs!!&J!A!"LG&K&JIs!!&J!A!%LG&K!@Is!#Ip!A!"LG&K!pIs!!&J!A!4LG&K!@Is!!&J!A!+LG&K!@Is!!&J!A!+LG&K"BIs!!>z!A!"LG&K#DIs!!&J!A!"LG&K!pIs!!&J!A!"LG&K$vIs!!&J!A!%LG&K!@Is!#Ip!A!:LG&K%y"<CDIs!#1@!A#)LG&K"BIs
!#A`!A!sLG&K%xIs!##e5g.Z!A!+LG&KB"Is!!&J!A!%LG&K!@Is!#A`!A"3LG&K/M"<$fIs!!&J!A!"LG&K!@Is!!&J!A"BLG&K!@Is!!&J!A!"LG&K!@Is!$6j!A!"LG&K!@Is!#9P!A!"LG&K!@Is!!&J!A!"LG&K9pIs!!6j!A"`LG&K&;"<%8Is!!6j!A"ELG&K"BIs!'>z!A!(LG&KLVJMLG&K$7"<%hIs!)A`!A"6LG&KLVJSLG&K
$7"<&:Is!)A`!A"6LG&KLVJPLG&K$7"<&jIs!)A`!A"6LG&KLVJMLG&K$7"<&jIs!)A`!A"6LG&KLVJMLG&K$7"<&jIs!)A`!A"6LG&KLVJMLG&K&;"<$fIs!!>z!A"BLG&K"rIs!'6j!A!+LG&KLVJMLG&K(?"<%8Is!!&J!A!"LG&K7lIs!!&J!A!"LG&K3dIs!!&J!A!"LG&KLVJPLG&K"S"<LVLVLM#d!A!*!(<6LVLV1PIs!!9Q5hLV
LVJsLG&K"S"<LVLVLM#d!A!Q

.TXT 5 -91 813 0 0
Cg a77.000000,77.000000,79
{\rtf\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\b Exercise 6:  Solving 
and equation\par }\par \tab Solve the following equation  for its roots}
.EQN 7 107 786 0 0
({0:x}NAME)^(3)-10*{0:x}NAME+2
.EQN 1 -84 812 0 0
({0:x}NAME)^(3)-10*{0:x}NAME+2