.MCAD 304020000 1 93 672 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 0 0 0 0 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 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 0 0 0 0 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 1 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 0.750000 0.300000 0.500000 0.500000 0 .CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* |P *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=1 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 5 20 343 0 0 0 Cg a27.000000,27.000000,28 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\fs28\b EG31 MATHCAD NOTES\par SESSION 1}} .TXT 7 -17 305 0 0 0 Cg a70.100000,70.100000,389 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b WHAT CAN BE DONE WITH MATHCAD?}{ \cf1 \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Combine the functionality of a spreadsheet with the WYSIWYG text and features of a word processor to generate a textbook-like document.\par \par }\pard \plain\s0\f0\fs20 \pard {\cf1 \tab 2. Update the entire document by making a change on any page.\par \par }\pard\plain\s0\f0\fs20 \pard { \cf1 \tab 3. Read data from a file and do mathematical operations such as adding a column of numbers , evaluating integrals or derivatives and invert matrices.}} .TXT 20 0 650 0 0 0 Cg a69.100000,69.100000,1137 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b GETTING AQUAINTED WITH THE MENUS AND TOOLS\par }{\cf1 \par \tab 1. Across the top of the Mathcad window are the pulldown menus:\par \par }\pard\plain\s0\f0\fs20 \pard { \cf1\ul F}{\cf1 ile }{\cf1\ul E}{\cf1 dit }{\cf1\ul V}{\cf1 iew }{ \cf1\ul I}{\cf1 nsert F}{\cf1\ul o}{\cf1 rmat }{\cf1\ul M}{\cf1 ath }{ \cf1\ul S}{\cf1 ymbolics }{\cf1\ul W}{\cf1 indow }{\cf1\ul H}{\cf1 elp\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. The second line contains the standard tool icons found in a word processor along with some additional ones for Mathcad. The function of each of these icons can be identified by placing the cursor on it, without clicking, and reading the prompt that appears \par }\pard\plain\s0\f0\fs20 \pard { \cf1 \par \tab 3. The Math tool palette consists of eight icons. These functions can also be identified by placing the cursor on the icon. Clicking once on any of these icons makes the related function window appear.\par \par \tab 4. The formatting toolbar, common to Microsoft Word and Excel appears just above the main Mathcad window. \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab To conserve screen space, any or all of the toolbars can be hidden or shown. To do this, click on the }{\cf1\ul V}{\cf1 iew menu and click on the }{\cf1\ul T}{ \cf1 oolbars selection with the cursor. This will expose a menu with the choices: }{\cf1\ul S}{\cf1 tandard, }{\cf1\ul F}{\cf1 ormatting and }{\cf1\ul M}{\cf1 ath. Clicking on one of these causes a check mark to either appear or disappear next to it and the corresponding toolbar to do likewise.\tab \tab }} .TXT 45 -3 616 0 0 0 C x1,1,0,0 .TXT 3 1 665 0 0 0 Cg a69.800000,69.800000,370 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b UNITS & PHYSICAL CONSTANTS\par } \pard\plain\s0\f0\fs20 \pard {\cf1\b \par \tab US}{\cf1 \tab \tab \tab \tab \tab }{\cf1\b CGS\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab feet (ft)}{\cf1\b \tab \tab \tab }{\cf1 \tab centimeter (cm)\par } \pard\plain\s0\f0\fs20 \pard {\cf1 \tab gram (gm)\tab \tab \tab pound (lb)\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab second (sec)\tab \tab \tab second (sec)\par \tab coulomb (coul)\tab \tab \tab coulomb (coul)\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab Kelvin (K)\tab \tab \tab \tab Kelvin (K)\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par }{ \cf1\b \tab SI}{\cf1 \tab \tab \tab \tab }{\object{\*\objclass \eqn} \rsltpict{\*\objdata .EQN 99 31 64 0 0 0 {0:MKS}NAME }}{\cf1 \tab \tab \tab \tab \tab \tab \tab \tab \par \tab meters (m) \tab \tab \tab meters (m)\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab kilogram (kg)\tab \tab \tab kilogram (kg)\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab second (sec)\tab \tab \tab second (sec)\par \tab amp (A)\tab \tab \tab \tab coulomb (coul)\par \tab Kelvin (K)\tab \tab \tab \tab Kelvin (K)\tab \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab \tab \tab candela (cd)\par }{\cf1 \tab \tab \tab mole (mole)}} .TXT 45 0 667 0 0 0 Cg a69.400000,69.400000,1180 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 Mathcad starts in SI units, unless the user specify some other system of units. \par \par }{\cf1\b To change the units:\par }{\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Choose }{\cf1\b\ul O}{\cf1\b ptions}{\cf1 from the }{\cf1\b Math}{ \cf1 pull down menu at the top of the \tab \tab Mathcad window.\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par \tab 2. Select the Units System tab at the top of the Math Options window. \par \par \tab 3. Click on whatever default system of units that you would like to use.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4. Click on the OK button at the bottom of the window to set the new units or click on the cancel button to keep the same ones.If you set the units system to None, you can define your own units in terms of the special built-in constants 1L, 1M, 1T, 1Q, 1K, 1C and 1S which represent the dimensions }{\cf1\i length, mass, time}{\cf1 }{\cf1\i charge or current, absolute temperature, luminosity}{\cf1 and }{\cf1\i substance}{ \cf1 .\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par }\pard\plain\s0\f0 \fs20 \pard {\cf1\b To display the units in the Mathcad worksheet:}{ \cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab \tab \tab \tab \tab \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Choose }{\cf1\b\ul O}{ \cf1\b ptions}{\cf1 from the }{\cf1\b Math}{\cf1 pull down menu at the top of the Mathcad window.\par \par }\pard\plain\s0\f0\fs20 \pard { \cf1 \tab 2. Click on the Dimensions tab at the top of the Math Options window\par \par \tab 3. Click on the box next to Display dimensions.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4. Click on the OK button at the bottom of the window to confirm the Display dimensions mode or click on the cancel button to keep the dimensions undisplayed on the Mathcad worksheet.\par }} .TXT 74 -1 241 0 0 0 Cg a72.100000,72.100000,238 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b A Simple Calculation\par }{\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click anywhere in the worksheet. You see a small crosshair. Anything you \tab type appears at the crosshair.\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par } \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. Type }{\cf1\b 15 - 8 / 104.4 =}{\cf1 . When you press the equals sign, Mathcad computes and \par \tab shows the results.}} .EQN 17 27 242 0 0 0 15-(8)/(104.5)={0}?_n_u_l_l_ .TXT 5 -20 668 0 0 0 Cg a56.600000,56.600000,611 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 As you type the equation, Mathcad shows a small rectangular box called the }{\cf1\b placeholder}{\cf1 . This holds spaces open for numbers or expressions not yet typed. As soon as you type a number, it replaces the placeholder in the equation. \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 3. Once an equation is on the screen, you can edit it by clicking on the appropriate spot and typing new letter, digits or operators. \par \tab \par 4. You can type many operators and Greek letters by clicking on the Greek}{\cf1\b }{\cf1 letters in the }{\cf1\b Math toolbar}{\cf1 to make the }{\cf1\b Greek letter palette}{\cf1 appear. Then simply click on the Greek letter you wish to appear at the placeholder in your equation.}} .TXT 27 -6 358 0 0 0 Cg a71.000000,71.000000,388 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Defining Variables}{\cf1 \par \par \tab To clear any previous equation and define a variable }{\cf1 \b t}{\cf1 , follow these steps:\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click in the equation you just typed and press [Space] until the entire expression is \tab held between the two editing lines.\par \par \tab 2. Chose Cu}{\cf1\ul t}{\cf1 for the }{ \cf1\ul E}{\cf1 dit menu.\par \par \tab 3. To begin defining }{\cf1\b t}{ \cf1 , type t: (the letter t followed by a colon). Mathcad shows the \tab \tab colon as the definition symbol :=}} .EQN 24 26 245 0 0 0 {0:t}NAME:_n_u_l_l_ .TXT 6 -26 246 0 0 0 Cg a71.400000,71.400000,73 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4. Type }{\cf1\b 10}{\cf1 in the empty placeholder to complete the definition for }{\cf1\b t }{ \cf1 .}} .EQN 4 26 247 0 0 0 {0:t}NAME:10 .TXT 6 -26 248 0 0 0 Cg a72.100000,72.100000,388 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab If you make a mistake, click on the equation and press [Space] until the entire expression is \tab between the two editing limes, as you did earlier. Then delete it by choosing }{\cf1\b Cu}{\cf1\b\ul t}{\cf1 from the }{\cf1\ul E}{\cf1 dit \tab menu.\par \par \tab To enter another definition:\par \par \tab 1. Press the Enter key. This moves the crosshair below the first equation.\par \par \tab 2. To define }{\cf1\b acc}{\cf1 as -9.8, type }{\cf1\b acc : -9.8}{\cf1 . Then press the Enter key again.}} .EQN 22 25 249 0 0 0 {0:t}NAME:10 .EQN 4 0 250 0 0 0 {0:acc}NAME:-9.8 .TXT 6 -25 251 0 0 0 Cg a71.000000,71.000000,559 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Calculating Results}{\cf1 \par \par \tab Now that the variables }{\cf1\b t}{\cf1 and }{\cf1\b acc}{ \cf1 are defined, they can be used in other expressions.\par \par \tab 1. Use the mouse to place the cursor a few line below the two definitions and click.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. Type }{\cf1\b acc / 2[Space] * t ^ }{\cf1\b 2}{\cf1 . the caret symbol ( }{\cf1\b ^}{\cf1 ) represents raising to a power. The \tab asterisk ( }{\cf1\b *}{\cf1 ) is multiplication and the slash ( }{\cf1\b /}{\cf1 ) represents division. Placing the space after \tab the }{\cf1\b 2}{\cf1 lets Mathcad know that the }{\cf1\b *t}{ \cf1 does not belong in the denominator but is to multiple the \tab complete previous expression.\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par \tab 3. Press the equal sign key ( }{\cf1\b =}{\cf1 ).}} .EQN 33 24 360 0 0 0 ({0:acc}NAME)/(2)*({0:t}NAME)^(2)={0}?_n_u_l_l_ .TXT 6 -24 361 0 0 0 Cg a72.100000,72.100000,184 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab This equation calculates the distance traveled by a falling body in time t with acceleration acc. \tab \tab We had previously defined }{\cf1\b t = 10}{\cf1\b seconds}{ \cf1 and }{\cf1\b acc = -9.8 meters per second squared}{\cf1 .}} .TXT 8 -1 617 0 0 0 C x1,1,0,0 .TXT 3 1 254 0 0 0 Cg a71.300000,71.300000,690 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Entering Text\par }{\cf1 \par } \pard\plain\s0\f0\fs20 \pard {\cf1 \tab To enter text, you click in an empty space and do one of the following: choose Text Region \tab from the Insert menu or press the double-quote key ( }{\cf1\b "}{\cf1 ). \par \par \tab Now do the following:\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click in the blank space to the right of the equations you entered. You will see a small \tab crosshair.\par \par \tab 2. Press }{\cf1\b "}{\cf1 to tell Mathcad that you're about to enter some text. The crosshair is changed into \tab a vertical line called the }{\cf1\b insertion point}{\cf1 . the characters that you type appear behind this line. \tab A box surrounds the insertion point, indicating that you are now in a text region. This box is \tab called the }{\cf1\b text box}{\cf1 . It grows as you enter text.\par \par \tab 3. Type the words: }{\cf1\b Equations of motion}{\cf1 . }} .EQN 36 23 255 0 0 0 {0:t}NAME:10 .EQN 4 0 256 0 0 0 {0:acc}NAME:-9.8 .TXT 1 19 257 0 0 0 Cg a30.100000,30.100000,19 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 Equations of motion}} .EQN 3 -19 258 0 0 0 ({0:acc}NAME)/(2)*({0:t}NAME)^(2)={0}?_n_u_l_l_ .TXT 5 -23 259 0 0 0 Cg a71.100000,71.100000,112 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4. To enter a second line of text, press the enter key and continue to type:\par \tab \tab }{\cf1\b for falling body under gravity}{\cf1 .}} .EQN 6 23 260 0 0 0 {0:t}NAME:10 .EQN 4 0 261 0 0 0 {0:acc}NAME:-9.8 .TXT 2 19 262 0 0 0 Cg a19.500000,19.500000,51 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 Equations of motion\par for falling body under gravity }} .EQN 2 -19 263 0 0 0 ({0:acc}NAME)/(2)*({0:t}NAME)^(2)={0}?_n_u_l_l_ .TXT 8 -23 264 0 0 0 Cg a68.500000,68.500000,206 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 5. To move out of the text box, click on a different spot on the worksheet or press\par \tab \tab [}{ \cf1\b Shift}{\cf1 ][}{\cf1\b Enter}{\cf1 ].\par \par \tab 6. To edit the text after leaving the text box, simply click on the text to reactive the text box.}} .TXT 43 -1 613 0 0 0 C x1,1,0,0 .TXT 3 1 265 0 0 0 Cg a70.900000,70.900000,808 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Iterative Calculations\par }{\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab Mathcad can do repeated or iterative calculations as easily as individual ones. It uses a special variable called a }{\cf1\b range variable}{\cf1 to perform iterations.\par \par \tab Range variables take on a range of values, such as the integers form 0 to 10. Whenever a range variable appears in a Mathcad equation, Mathcad calculates the equation once for each value of the range variable.\par \par \tab To compute equations for a range of values, first create a }{\cf1\b range variable}{\cf1 . In this case, we will compute the results for a range of values of }{\cf1 \b t}{\cf1 from 10 to 20 in steps of 1.\par \par }\pard\plain\s0\f0 \fs20 \pard {\cf1 \tab 1. change t into a range variable by editing its definition. Click on the 10 in the \tab \tab equation t : = 10. The insertion point should be next to the 10.\par \par \tab 2. Type }{ \cf1\b , 11}{\cf1 . This tells Mathcad that the next number in the range will be 11.}} .EQN 33 23 618 0 0 0 {0:t}NAME:10,11 .TXT 9 -23 267 0 0 0 Cg a71.000000,71.000000,355 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 3. Type }{\cf1\b ;20}{\cf1 . This tells Mathcad that the last number in the range will be }{\cf1\b 20}{ \cf1 . Mathcad \tab \tab shows the semicolon as a pair of dots. Clicking outside the equation for }{\cf1\b t}{\cf1 \tab \tab \tab causes Mathcad to compute with }{\cf1\b t}{\cf1 defined as a range variable. Since }{\cf1\b t}{\cf1 takes \tab on eleven different values, there must be eleven different answers. These are \tab \tab \tab displayed in the table .}} .EQN 12 23 268 0 0 0 {0:t}NAME:10,11;30 .EQN 1 26 614 0 0 0 ({0:acc}NAME)/(2)*({0:t}NAME)^(2)={0}?_n_u_l_l_ .EQN 3 -26 269 0 0 0 {0:acc}NAME:-9.8 .TXT 49 -23 619 0 0 0 Cg a71.800000,71.800000,223 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 Mathcad displays on the first 16 rows of the table of calculated\par values. Single-clicking on the table displays horizontal and\par vertical scroll bars which can be used to view any group of 16\par rows of the calculated values. }} .TXT 12 0 271 0 0 0 Cg a78.000000,78.000000,391 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Defining a Function}{\cf1 \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab Additional flexibility can be gained by defining functions. Here is how to add a function to your worksheet:\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. First, delete the table. To do so, click anywhere in the table and press the [Space] bar until everything \tab is enclosed between the two editing lines.\par \par \tab 2. Define the function }{\cf1\i d(t)}{ \cf1 by typing }{\cf1\b d( t ) :\par \tab }{\cf1 and the expression : }{ \cf1\b 1600 + acc / 2 [Space] * t ^ 2}} .EQN 25 20 272 0 0 0 {0:d}NAME({0:t}NAME):1600+({0:acc}NAME)/(2)*({0:t}NAME)^(2) .TXT 5 -20 273 0 0 0 Cg a71.100000,71.100000,281 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab The definition just typed defines a function with the name }{\cf1\b d}{\cf1 with the argument }{ \cf1\b t}{\cf1 . \par \tab This function can be used to evaluate the expression for different values of }{\cf1\b t}{\cf1 .\par \par \tab To evaluate the function at the value 3.5, type }{\cf1\b d ( 3.5 ) =}{\cf1 . \par \tab Mathcad returns the correct value as shown below.}} .EQN 12 20 274 0 0 0 {0:d}NAME(3.5)={0}?_n_u_l_l_ .TXT 3 -20 275 0 0 0 Cg a75.400000,75.400000,214 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab To evaluate the function once for each value of t defined earlier, click below the equation\par \tab and type }{\cf1\b d ( t )=}{\cf1 . \par }\pard\plain\s0\f0\fs20 \pard { \cf1 \tab Mathcad shows a table of values. The first two values are in exponential (powers of 10) notation.}} .EQN 9 23 606 0 0 0 {0:d}NAME({0:t}NAME)={0}?_n_u_l_l_ .TXT 68 -23 672 0 0 0 Cg a71.000000,71.000000,991 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Formatting a Result\par }{\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab The display format can be set for any number that Mathcad calculates and displays. The previous table can be changed so that none of the numbers are displayed in exponential notation.\par }\pard\plain\s0\f0\fs20 \pard { \cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click on the table with the mouse and choose }{\cf1\b Number}{\cf1 from the }{\cf1 \b F}{\cf1\b\ul o}{\cf1\b rmat}{\cf1 menu. The \tab Format Number dialog box is displayed. The number of decimal places, the use of \tab exponential notation and whether the number is shown in decimal, octal, or hexadecimal can \tab be selected as settings. The option button beside "Set for current region only:" should be filled \tab in. The Format Number dialog box can also be displayed by double-clicking on the table.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. The default setting for Exponential Threshold is 3. This means that only numbers greater or \tab equal to 10}{\cf1\up 3}{\cf1 are displayed in exponential notation. Click to the right of the }{\cf1\b 3}{ \cf1 , press [}{\cf1\b BkSp}{\cf1 ] \tab and type }{\cf1\b 6}{\cf1 . Then click the "OK" button. The table changes to reflect the new format and 1110 \tab is no longer shown in exponential notation.}} .EQN 33 27 666 0 0 0 {0:d}NAME({0:t}NAME)={0}?_n_u_l_l_ .TXT 79 -28 620 0 0 0 C x1,1,0,0 .TXT 3 1 307 0 0 0 Cg a71.300000,71.300000,634 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Graphs \par }{\cf1 \par }\pard \plain\s0\f0\fs20 \pard {\cf1 \tab Mathcad can show both two-dimensional Cartesian and polar graphs, contour plots, surface \tab plots and a variety of other two dimensional plots. These are all done in a plot region.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab }{\cf1\b To create a graph}{\cf1 \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click in a blank space where you would like to locate the graph and type the expression for the dependent expression which is to appear on the y-axis of your plot. Type d ( t ) and be sure that the editing lines remained displayed on the expression.\tab \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. Choose }{\cf1\b Graph=>X-Y Plot}{\cf1 form the }{ \cf1\b Insert}{\cf1 menu. This will produce an empty graph with placeholders on the x-axis and y-axis for the expressions to be graphed. \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab \tab }} .EQN 33 19 363 0 0 0 _n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&{0:d}NAME({0:t}NAME)@_n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&_n_u_l_l_ 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 0 0 0 0 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 14 0 3 .TXT 24 -19 309 0 0 0 Cg a71.100000,71.100000,160 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 3. Type in}{\cf1\b t}{\cf1 at the placeholder on the x-axis of the graph. Click anywhere \tab \tab \tab outside the graph and Mathcad calculates and graphs the points as shown below. }} .EQN 7 19 385 0 0 0 {0:t}NAME:10,11;20 .EQN 3 0 386 0 0 0 {0:acc}NAME:-9.8 .EQN 4 0 387 0 0 0 {0:d}NAME({0:t}NAME):1600+({0:acc}NAME)/(2)*({0:t}NAME)^(2) .TXT 0 22 392 0 0 0 Cg a34.100000,34.100000,49 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 Equation of motion for falling\par body under gravity}} .EQN 5 -22 389 0 0 0 {0:d}NAME(3.5)={0}?_n_u_l_l_ .EQN 3 0 390 0 0 0 {0:d}NAME({0:t}NAME)={0}?_n_u_l_l_ .EQN 7 16 391 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:d}NAME({0:t}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:t}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 1 1 1 1 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 14 0 3 .TXT 27 -36 621 0 0 0 C x1,1,0,0 .TXT 3 1 370 0 0 0 Cg a71.300000,71.300000,934 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab }{\cf1\b Resizing a graph}{\cf1 \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click the mouse just outside the graphics region to anchor one corner of the selection \tab rectangle.\par \par \tab 2. Press and hold down the mouse button and drag the mouse toward the plot region. A \tab dashed selection rectangle emerges from the anchor point.\par \par \tab 3. With the selection rectangle just enclosing the graphics region, let go of the mouse button. \tab The dashed rectangle will turn into a solid rectangle with handles.\par \par \tab 4. Move the mouse pointer to any of the handles. When it is properly positioned, it will turn into \tab a double-headed arrow.\par \par \tab 5. Press down and hold the mouse button and move the mouse to stretch the graphics region \tab in that direction.\par \par \tab 6. Once the graphics region is the right size, let go of the mouse button.\par \par \tab 7. This operation can be repeated with any of the handles.\par \par \tab 8. When the graph has been stretched to the desired size, click outside of the graphics region \tab to deselect it.}} .EQN 55 20 349 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:d}NAME({0:t}NAME)@&15&(_n_u_l_l_&_n_u_l_l_)&{0:t}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 1 1 1 0 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 33 35 14 0 3 .TXT 55 -21 622 0 0 0 C x1,1,0,0 .TXT 4 1 356 0 0 0 Cg a71.500000,71.500000,4306 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Zooming in on a portion of a graph\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1\b \tab }{\cf1 Sometimes it is desireable to be able to zoom in on a portion of a graph in order to find out details such as the value(s) at the intersection of two plotted equations. These types of points are of interest since they are the set(s) of values that are the solution to both equations.\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par \tab \tab }{ \cf1\b Zooming Method 1:\par }{\cf1 \par }\pard\plain\s0\f0\fs20 \pard { \cf1 \tab 1. Click on the graph so that it appears in the solid boarder with handles. It also has \tab numerical values at the extremes of each of its axes in addition to the usual values along each \tab of the axes. \par \par \tab 2. Click on the leftmost value for the horizontal axis. A cursor appears in that location.\par \par \tab 3. Press the }{\cf1\b Delete}{\cf1 key to remove the present value of }{\cf1\b 10}{\cf1 and replace it with a }{\cf1\b placekeeper }{\cf1 .\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4. Type in }{ \cf1\b 1}{\cf1\b 5}{\cf1 and press the }{\cf1\b Enter}{\cf1 key. The leftmost value on the horizontal scale is changed \tab from the default value of 10 to 15. The graph has now zoomed in on the portion of the data \tab between the values of 15 and 20. \par \par \tab \tab Note: The same steps are used to zoom out on a graph. However, the graph will only \tab plot the values which are defined by the original range variable and the resulting values \tab computed for the dependent variable. It will not extrapolate the plot to the new range.\par \par \tab \tab }{\cf1\b Zooming Method 2:}{\cf1 \par \par \tab 1. Click on the graph to select it.\par \par \tab 2. In the }{ \cf1\b F}{\cf1\b\ul o}{\cf1\b rmat}{\cf1 menu at the top of the window, choose }{\cf1\b\ul G}{\cf1\b raph}{\cf1 and then }{\cf1\b\ul Z}{ \cf1\b oom}{\cf1 .\par \tab This causes the X-Y dialog box to appear. \par \par \tab 3. If needed, the dialog box can be repositioned, using the mouse, to allow the complete \tab graph to \tab be seen. \par \par \tab 4. Within the graph region, place the mouse at a location which locates one corner of a \tab box that \tab you want to draw to describe the region you want to magnify.\par \par \tab 5. Press and hold the mouse button down as you define the box around the area to be \tab magnified by dragging the mouse through a diagonal path to describe the region to be \tab \tab magnified. A dashed rectangle appears as you drag the mouse to indicate the region. \par \par \tab 6. If necessary, the region can be repositioned by positioning the cursor in the dashed \tab \tab box, pressing and hold the mouse button and move the mouse to reposition the dashed \tab rectangle.\par \par \tab Note that the coordinates of the corners of the dashed box are displayed in the X-TY \tab \tab Zoom dialog box and that they change as dashed box is moved.\par \par \tab 7. Clicking on the Zoom button redraws the graph within the dahed box as the full graph.\par \par \tab 8. The limits of the axes are those of the dashed box. However, they can be changed \tab \tab as described in Zooming Method 1, above.\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par } \pard\plain\s0\f0\fs20 \pard {\cf1 \par \par }{\cf1\b To unzoom a graph that has already been zoomed but which the axis limits have not been changed.\par }\pard\plain\s0\f0\fs20 \pard {\cf1\b \par }\pard \plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click on the graph to activate its graph region.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. Choose }{\cf1\b\ul G}{\cf1\b raph}{\cf1 => }{\cf1\b\ul Z}{\cf1\b oom}{ \cf1 from the }{\cf1\b F}{\cf1\b\ul o}{\cf1\b rmat}{\cf1 menu to bring up the X-Y Zoom box.\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 3. Click on the }{\cf1 \b\ul U}{\cf1\b nzoom}{\cf1 button to get back to the previous level of zoom or click on the }{\cf1\b\ul \tab F}{\cf1\b ull View}{\cf1 button to see the original graph prior to any zooming.\par \par \par }{ \cf1\b G}{\cf1\b raph coordinates\par \par \par }{\cf1 To see a readout of the graph coordinates that make up a trace:\par \par \tab 1. Click on the graph region to select it.\par \par \tab 2. Choose }{ \cf1\b\ul G}{\cf1\b raph}{\cf1 => }{\cf1\b\ul T}{\cf1\b race}{\cf1 from the }{\cf1\b F}{\cf1\b\ul o}{\cf1\b rmat}{\cf1 menu, or clic on the Trace button on the \tab \tab Graph Palette, to show the X-Y Trace dialog box. Reposition the box so that \tab the entire graph can be seen, if necessary. Note that the Track Data Points \tab \tab \tab box is checked.\par \par \tab 3. In the graph region, click and drag the mouse along the trace whose coordinates you \tab want to see. A dotted crosshair jumps from one point to the next as you move \tab along the trace.\par \par \tab 4. If the mouse button is released, the left and right arrrows can be used to move to the \tab \tab previous or next data points. The up and down arrows move to other traces on \tab \tab the same graph.\par \par \tab 5. As the pointer reaches each point on the trace, Mathcad displays the x and y values \tab \tab of that point in the X-Value and Y-Value boxes.\par \par \tab 6. The coordinate values of the last selected point remain in the boxes. The crosshair \tab \tab remains until you click outside the graph.\par \par To copy a coordinate to the clipboard:\par \par } \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Click "Copy X "or "Copy Y". The value can then be pasted into a math region or a \tab \tab \tab text region on the Mathcad worksheet, into a spreadsheet, or into any other \tab \tab \tab application that allows pasting from the clipboard.\par \par \tab 2. Click outside the graph or on the "Close" button to make the crosshairs disappear.}} .TXT 238 0 322 0 0 0 Cg a71.500000,71.500000,994 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Formatting a graph}{\cf1 \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab A graph is produced with default characteristics: numbered linear axes, no grid lines and points connected with solid lines. These characteristics can be changed for formatting the graph.\par }\pard\plain\s0\f0\fs20 \pard { \cf1 \tab \tab \tab \par \tab To do this:\par \par }\pard\plain\s0\f0 \fs20 \pard {\cf1 \tab 1. Double-click on the graph to bring up the appropriate dialog box. This box contains \tab \tab settings for all available plot format options. \par \par \tab 2. Click on the }{\cf1 \b Traces}{\cf1 tab in the dialog box to see the correct page.\par \par \tab 3. Click on "trace 1" in the scrolling list under "Legend Label". Mathcad places the \tab \tab current settings for trace 1 in the boxes under the corresponding columns of the scrolling \tab list. \par \par \tab 4, Click on the arrow under the "Type" column to see a drop-down list of trace types.\par \par \tab 5. Choose "bar" from this drop-down list by clicking on it.\par \par \tab 6. Click on the "OK" button to show the result of changing the setting. Mathcad shows \tab \tab the graph as a bar chart instead of connecting the points with lines. \par \par \tab 7. Click outside the graph to deselect it. }} .EQN 57 14 323 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:d}NAME({0:t}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:t}NAME 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 3 1 1 NO-TRACE-STRING 0 1 1 1 1 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 33 35 14 0 3 .TXT 63 -14 625 0 0 0 Cg a71.100000,71.100000,1505 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Building Expressions}{\cf1 \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab Mathematical expressions can be created in Mathcad by simply typing in a stream of characters. Characters like }{\cf1\b *}{\cf1 and }{\cf1\b +}{\cf1 represent operators.\par \par \tab Mathcad behaves a lot like a standard word processor. As you type, characters appear behind a vertical editing line. There are, two important differences:\par \par }{\cf1 \tab 1. As the editing line moves to the right, it leaves behind a horizontal editing line.\par \par \tab 2. Unless you have clicked on an equation that already has an operator in it, pressing \tab \tab the [Space] bar will turn the the math region into a text region. You cannot turn a text \tab \tab region back into a math region.\par \par \tab }{\cf1\b Typing in operators\par }{\cf1 \par \tab Operators like the symbols }{ \cf1\b +}{\cf1 and }{\cf1\b -}{\cf1 link variables and numbers to form expressions. These expressions are called }{\cf1\b operand}{\cf1 \b s}{\cf1 . The key to working with operators is learning to specify which variable or expression is to become the operand. This can be done in two ways:\par \par \tab 1. You can type the operator first and fill in the placeholders with operands.\par \par \tab 2. You can learn how to use the editing lines to specify what variables or expression \tab \tab \tab you want to turn into an operand.\par \par Try creating the expression a }{\cf1\up x+y}{\cf1 using the first method:\par \par \tab 1. Press ^ to create the exponent operator. It appears with two placeholders.\par \par \tab \tab \tab \tab \tab \tab \tab \tab \par \tab \par \tab 2. Click in the lower placeholder and type the letter }{\cf1\b a}{\cf1 . \par \par \par \tab \tab \tab \tab \tab \tab \tab \tab }{\object{\*\objclass \eqn}\rsltpict{ \*\objdata .EQN 1493 49 330 0 0 0 ({0:a}NAME)^(_n_u_l_l_) }}{\cf1 \par \tab 3. Click in the upper placeholder and type }{\cf1 \b +}{\cf1 .\par \par \tab \tab \tab \tab \tab \tab \tab \tab }{ \object{\*\objclass \eqn}\rsltpict{\*\objdata .EQN 1500 49 331 0 0 0 ({0:a}NAME)^(_n_u_l_l_+_n_u_l_l_) }}{\cf1 \par \par \tab 4. Click in the remaining placeholders and type }{\cf1\b x}{\cf1 and }{\cf1\b y}{\cf1 .\par \par \tab \tab \tab \tab \tab \tab \tab \tab }{\object{\*\objclass \eqn}\rsltpict{ \*\objdata .EQN 1508 49 332 0 0 0 ({0:a}NAME)^({0:x}NAME+{0:y}NAME) }}{\cf1 \par \par \tab \tab }} .EQN 63 21 627 0 0 0 (_n_u_l_l_)^(_n_u_l_l_) .EQN 0 35 629 0 0 0 (_n_u_l_l_)^(_n_u_l_l_) .TXT 50 -57 630 0 0 0 C x1,1,0,0 .TXT 3 2 335 0 0 0 Cg a70.100000,70.100000,749 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 Now try creating the same expression using the editing lines.\par \par \tab 1. Type }{\cf1\b a}{ \cf1 . The line beneath the }{\cf1\b a }{\cf1 indicates the }{ \cf1\b a}{\cf1 will be the first operand of \tab \tab \tab whatever operator you type.\par \par \tab \tab \tab \tab \tab \tab \tab \tab }{ \object{\*\objclass \eqn}\rsltpict{\*\objdata .EQN 1556 50 336 0 0 0 {0:a}NAME }}{\cf1 \par \par \tab 2. Press ^ to create the exponent operator. The editing lines now surround the new \tab \tab \tab placeholder.\par \par \par \tab \tab \tab \tab \tab \tab \tab \tab }{\object{ \*\objclass \eqn}\rsltpict{\*\objdata .EQN 1567 50 337 0 0 0 ({0:a}NAME)^(_n_u_l_l_) }}{\cf1 \par \par \tab 3. Type x + y in this placeholder to complete the expression.\par \par \tab \tab \tab \tab \tab \tab \tab \tab }{\object{\*\objclass \eqn}\rsltpict{\*\objdata .EQN 1576 50 338 0 0 0 ({0:a}NAME)^({0:x}NAME+{0:y}NAME) }}{\cf1 \par \par \par \par Now type the expression }{\cf1\b a}{\cf1 \b\up x}{\cf1\b + y }{\cf1 instead of }{\cf1\b a}{\cf1\b\up x+y }{ \cf1\up .\par \par }{\cf1 \tab 1. Type }{\cf1\b a^x}{\cf1 .\par \par \par \tab \tab \tab \tab \tab \tab \tab \tab }{\object{ \*\objclass \eqn}\rsltpict{\*\objdata .EQN 1594 50 339 0 0 0 ({0:a}NAME)^({0:x}NAME) }}{\cf1 \par \par \tab 2. Press the [Space] bar to cause the editing line to hold the entire expression.\par \par \tab 3. Now type }{\cf1 \b +}{\cf1 . Whatever was held between the editing lines has now become the \tab \tab \tab first operand of the plus sign.\par \par \tab \tab \tab \tab \tab \tab \tab \tab }{\object{\*\objclass \eqn} \rsltpict{\*\objdata .EQN 1608 50 341 0 0 0 ({0:a}NAME)^({0:x}NAME)+_n_u_l_l_ }}{\cf1 \par \par \tab 4. In the remaining placeholder, type }{\cf1\b y}{ \cf1 .\par \par \tab \tab \tab \tab \tab \tab \tab \tab }{\object{ \*\objclass \eqn}\rsltpict{\*\objdata .EQN 1616 50 342 0 0 0 ({0:a}NAME)^({0:x}NAME)+{0:y}NAME }}} .TXT 104 -2 631 0 0 0 C x1,1,0,0 .TXT 3 18 473 0 0 0 Cg a32.500000,32.500000,34 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\fs28\b EG 31 MATHCAD EXERCISES\par } \pard\plain\s0\f0\fs20 \pard {\cf1\fs28\b SESSIONS 1}} .TXT 9 -17 513 0 0 0 Cg a71.600000,71.600000,324 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Exercise 1 : Units }{\cf1\b Conversion}{ \cf1 \par \par \tab \tab \tab \tab \tab \tab \par }\pard\plain\s0\f0 \fs20 \pard {\cf1 \tab 1. Go to options in the Math pull down menu. Select the Dimensions tab and click on \tab \tab \tab the box next to "Display dimensions".\par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab \tab \tab \tab \tab \par \tab 2. In the box next to "}{\cf1\ul M}{\cf1 ass" type }{\cf1\b kg}{\cf1 . In the box next to "}{\cf1\ul L}{\cf1 ength" type }{\cf1\b m}{\cf1 . In the box \tab \tab \tab next to "}{ \cf1\ul T}{\cf1 ime" type }{\cf1\b sec}{\cf1 .\par \par }\pard \plain\s0\f0\fs20 \pard {\cf1 \tab 3. Type in the following:\tab \tab \tab }} .EQN 22 33 475 0 0 0 {0:mass}NAME:75*{0:kg}NAME .EQN 5 -1 476 0 0 0 {0:acc}NAME:100*({0:m}NAME)/(({0:sec}NAME)^(2)) .EQN 6 0 477 0 0 0 {0:acc_g}NAME:9.8*({0:m}NAME)/(({0:sec}NAME)^(2)) .EQN 5 0 478 0 0 0 {0:F}NAME:{0:mass}NAME*({0:acc}NAME+{0:acc_g}NAME) .TXT 6 -32 479 0 0 0 Cg a71.500000,71.500000,52 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab \tab \tab \tab \tab 4. Now type }{\cf1\b F =}{\cf1 to get the answer with units: }} .EQN 5 32 480 0 0 0 {0:F}NAME={0}?_n_u_l_l_ .TXT 3 -32 481 0 0 0 Cg a71.800000,71.800000,119 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 To change the units:\par \par } \pard\plain\s0\f0\fs20 \pard {\cf1 \tab Click on the placeholder to the right of the units and type in }{\cf1\b dyne}{\cf1 and press the Enter \tab \tab \tab key.}} .EQN 10 32 632 0 0 0 {0:F}NAME={0}?{0:dyne}NAME .TXT 4 -32 483 0 0 0 Cg a71.500000,71.500000,227 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Exercise 2: X-Y plots\par \par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Define the range of the variable }{\cf1\b x}{\cf1 to start at }{\cf1\b -8 }{\cf1 and end at }{\cf1\b +8}{\cf1 and to increment \tab \tab \tab by }{\cf1 \b 0.1\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. Define the equation for the dependent variable }{\cf1\b y(x)}{\cf1 as }{\cf1 \b 3x}{\cf1\b\up 3}{\cf1\b + 7x +3\par }\pard\plain\s0\f0\fs20 \pard { \cf1\b \tab \tab \tab \tab \tab \par }\pard\plain\s0\f0\fs20 \pard { \cf1 \tab 3. Plot the graph.}} .EQN 1 93 653 0 0 0 {0:x}NAME:-8,-7.9;8 .EQN 4 0 654 0 0 0 {0:y}NAME({0:x}NAME):3*({0:x}NAME)^(3)+7*{0:x}NAME+3 .EQN 14 -61 486 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME({0:x}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:x}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 1 1 1 1 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 14 0 3 .TXT 28 -33 534 0 0 0 Cg a73.000000,73.000000,77 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4. Redefine the range of the variable }{\cf1\b x}{\cf1 to start at }{\cf1\b -5}{\cf1 and end at }{\cf1\b +5}{\cf1 .}} .EQN 4 29 538 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME({0:x}NAME)@5&-5&(_n_u_l_l_&_n_u_l_l_)&{0:x}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 1 1 0 0 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 14 0 3 .TXT 29 -28 487 0 0 0 Cg a66.000000,66.000000,71 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \par \tab 5. Add the title }{\cf1 \b X-Y PLOT }{\cf1 (Hint: double click on the graph)\par \par \tab \tab \tab \tab \tab }} .EQN 9 28 533 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME({0:x}NAME)@5&-5&(_n_u_l_l_&_n_u_l_l_)&{0:x}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 1 1 0 0 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 14 0 3 X-Y PLOT .TXT 27 -28 489 0 0 0 Cg a70.000000,70.000000,79 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 6. Deselect Autoscale\par \par \tab 7. Change the plotted line to a dashed line.\par \par \tab \tab \tab \tab \tab }} .EQN 9 28 532 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME({0:x}NAME)@5&-5&(_n_u_l_l_&_n_u_l_l_)&{0:x}NAME 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 3 0 0 1 1 NO-TRACE-STRING 0 1 1 0 0 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 14 0 3 X-Y PLOT .EQN 40 64 655 0 0 0 {0:x}NAME={0}?_n_u_l_l_ .EQN 0 6 656 0 0 0 {0:y}NAME({0:x}NAME)={0}?_n_u_l_l_ .TXT 2 -98 491 0 0 0 Cg a71.800000,71.800000,83 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 8. Change the number of grid line on the }{\cf1\b x}{\cf1 axis to 10 and the }{\cf1\b y(x)}{\cf1 axis to 4.\tab \tab \tab \tab }} .EQN 4 28 529 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME({0:x}NAME)@5&-5&(_n_u_l_l_&_n_u_l_l_)&{0:x}NAME 0 0 1 1 0 10 0 1 1 0 0 1 1 0 4 0 1 1 0 3 0 0 1 1 NO-TRACE-STRING 0 1 1 0 0 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 14 0 3 X-Y PLOT .TXT 28 -28 493 0 0 0 Cg a71.500000,71.500000,69 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 9. Generate a table of x and y values by typing : }{\cf1\b x =}{\cf1 and }{\cf1\b y(x) =}{\cf1 }} .TXT 6 0 558 0 0 0 Cg a71.800000,71.800000,313 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Exercise 3: Finding the zero of a function using a graph}{\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Plot the function }{ \cf1\b y(x) = 3x}{\cf1\b\up 3}{\cf1\b + 7x + 3}{\cf1 over the range of }{\cf1\b -8}{\cf1 to }{\cf1\b 8}{\cf1 in increments of }{\cf1\b 0.1\par }\pard\plain\s0\f0\fs20 \pard {\cf1\b \par }{\cf1 \tab 2. Adjust the }{\cf1\b x}{\cf1 axis to the range with grid lines at an interval of }{\cf1\b 2}{\cf1 units.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 3. Adjust the }{\cf1\b y(x)}{\cf1 axis to the range with gridlines at an interval }{\cf1\b 400 }{\cf1 units.\tab \tab \tab \tab }} .EQN 19 28 571 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME({0:x}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:x}NAME 0 0 1 1 0 10 0 1 1 0 0 1 1 0 10 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 1 1 1 1 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 19 14 0 2 .TXT 32 -28 560 0 0 0 Cg a71.800000,71.800000,91 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4. From this plot, estimate the value of }{\cf1\b x}{\cf1 where the value of }{\cf1\b y(x)}{ \cf1 equals zero.\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab \tab \tab \tab \tab }} .TXT 29 0 637 0 0 0 Cg a71.500000,71.500000,123 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 5. Create a new plot which has a narrower range for the values of x and y so that you \tab \tab can zoom-in and add gridlines}} .EQN 7 7 561 0 0 0 8&-8&(_n_u_l_l_&_n_u_l_l_)&{0:y}NAME({0:x}NAME)@1&-1&(_n_u_l_l_&_n_u_l_l_)&{0:x}NAME 0 1 1 1 0 10 0 1 1 0 1 1 1 0 10 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 0 0 0 0 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 52 19 14 0 2 .TXT 31 -7 562 0 0 0 Cg a71.800000,71.800000,112 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 6. Continue narrowing the range until you can view the value of }{\cf1\b x}{\cf1 for which the value of \tab \tab }{\cf1\b y(x)}{\cf1 is zero.}} .TXT 8 0 563 0 0 0 Cg a71.500000,71.500000,141 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}{\f1\fcharset2\fnil Symbol;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\b Exercise 4: Polar plots\par \par }\pard\plain\s0\f0\fs20 \pard {\cf1 \tab 1. Create a polar plot for the functions }{\cf1\b R(}{\cf1\f1\b q}{ \cf1\b )}{\cf1\b = sin(}{\cf1\f1\b q}{\cf1\b )}{\cf1 over the range of }{\cf1\b 0}{\cf1 to }{\cf1\b 2}{\cf1\f1\b p }{\cf1 in \tab \tab \tab increments of }{\cf1\b 0.1\tab \tab \tab \tab \tab }} .EQN 5 93 579 0 0 0 {0:\q}NAME:0,.1;2*{0:\p}NAME .EQN 3 0 580 0 0 0 {0:R}NAME({0:\q}NAME):{0:sin}NAME({0:\q}NAME) .EQN 3 -69 582 0 0 0 &&(_n_u_l_l_&_n_u_l_l_)&{0:R}NAME({0:\q}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:\q}NAME 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 1 1 1 1 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 16 16 0 20 3 .TXT 63 -24 642 0 0 0 Cg a71.500000,71.500000,56 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}{\f1\fcharset2\fnil Symbol;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 2. Repeat the plot using the function }{\cf1\b r}{\cf1\b (}{\cf1\f1\b q}{ \cf1\b )}{\cf1\b = }{\cf1\f1\b q}{\cf1\b }{\cf1\b sin(}{\cf1\f1\b q}{ \cf1\b )\par }} .EQN 0 91 657 0 0 0 {0:r}NAME({0:\q}NAME):{0:sin}NAME({0:\q}NAME) .EQN 3 -67 643 0 0 0 _n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&{0:r}NAME({0:\q}NAME)@_n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&{0:\q}NAME 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 0 0 0 0 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 16 16 0 20 3 .TXT 28 -23 567 0 0 0 Cg a76.000000,76.000000,67 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}{\f1\fcharset2\fnil Symbol;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 3.}{ \cf1\b }{\cf1 Repeat the plot using the function }{\cf1\f1\b r}{\cf1 \b (}{\cf1\f1\b q}{\cf1\b )}{\cf1\b = }{\cf1\b cos(}{\cf1\f1\b q)}{ \cf1\b }{\cf1\b sin(}{\cf1\f1\b q}{\cf1\b )\par \par \tab \tab \tab \tab \tab }} .EQN 1 91 658 0 0 0 {0:\r}NAME({0:\q}NAME):{0:cos}NAME({0:\q}NAME)*{0:sin}NAME({0:\q}NAME) .EQN 4 -67 568 0 0 0 _n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&{0:\r}NAME({0:\q}NAME)@_n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&{0:\q}NAME 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 0 0 0 0 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 16 16 0 20 3 .TXT 32 -25 569 0 0 0 Cg a71.900000,71.900000,106 {\rtf1\ansi \deff0{\colortbl;\red10\green36\blue106;}{\fonttbl{\f0 \fcharset0\fnil Arial;}{\f1\fcharset2\fnil Symbol;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 \tab 4.}{ \cf1\b }{\cf1 Repeat the plot using the function }{\cf1\f1\b r}{\cf1 \b (}{\cf1\f1\b q}{\cf1\b 1}{\cf1\b )}{\cf1\b = cos(4}{\cf1\f1\b q1)}{ \cf1\b }{\cf1\b sin(4}{\cf1\f1\b q1) }{\cf1 between 0 and 2}{\cf1\f1 p}{ \cf1 in \tab \tab \tab increments of .05}} .EQN 1 92 659 0 0 0 {0:\q1}NAME:0,.05;2*{0:\p}NAME .EQN 6 0 660 0 0 0 {0:\r1}NAME({0:\q1}NAME):{0:cos}NAME(4*{0:\q1}NAME)*{0:sin}NAME(4*{0:\q1}NAME) .EQN 3 -66 570 0 0 0 _n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&{0:\r1}NAME({0:\q1}NAME)@_n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&{0:\q1}NAME 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 0 0 0 0 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 16 16 0 20 3