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"on your tech drive " }{TEXT 220 165 "as number1.mws. Remember to sav e frequently in case the system shuts down in the middle of a work ses sion! Place your names and date at the top of your worksheet. W" } {TEXT 220 219 "hen you are satisfied that you have completed, and unde rstand the concepts covered in the worksheet, alert the instructor or \+ one of the TAs so that we can go through it with you and document that you have completed it. " }{TEXT 220 0 "" }}{PARA 232 "" 0 "" {TEXT 223 0 "" }}{PARA 211 "" 0 "" {TEXT 250 245 "We begin by experimenting \+ with some very basic calculations. The intent is to learn some basic \+ MAPLE syntax, while observing some of the neat features of a Computer \+ Algebra System (CAS). We will also review some basic concepts from ar ithmetic." }{TEXT 250 0 "" }}{PARA 232 "" 0 "" {TEXT 223 0 "" }}{PARA 211 "" 0 "" {TEXT 250 827 "Perform the following calculations with MAP LE. As you do these exercises enter notes and comments onto your work sheet in text mode. In particular, the author of these worksheets som etimes purposefully leaves off certain required MAPLE syntax. He is e ither sadistic or he is trying to make a point. Let's assume the latt er for now. The first such example is in the first problem below. A C AS requires some syntaxual thing to tell it when you are through givin g it instructions and are ready for it to do them. Try the first cal culation just as indicated, and note the error message. See if you ca n figure out what syntax is required by MAPLE to tell it that you are \+ ready for it to do its thing. (Place the cursor on the execution line \+ indicated by the symbol [> and type in your MAPLE instructions, a. k. \+ a. \"input.\")" }{TEXT 250 0 "" }}{PARA 211 "" 0 "" {TEXT 250 7 "1. 6 +2" }{TEXT 250 0 "" }}{EXCHG {PARA 232 "> " 0 "" {TEXT 223 0 "" }}} {PARA 211 "" 0 "" {TEXT 250 119 "Another example of \"omitted\" requir ed MAPLE syntax is in the next problem. It's more subtle and you may \+ have to ask." }{TEXT 250 0 "" }}{PARA 211 "" 0 "" {TEXT 250 10 "2. 2( 3+5)" }{TEXT 250 0 "" }}{EXCHG {PARA 232 "> " 0 "" {TEXT 223 0 "" }}} {PARA 228 "" 0 "" {TEXT 220 300 "Can you figure out just what MAPLE wa s doing to come up with the answer it gave for #2? In other words \"H ow did MAPLE interpret the operation 2(3+5)?\" To answer this try so me more examples like 2(34), 2(x-6), 2(t). (You can always get a new e xecution line by clicking on [> from the toolbar and " }{TEXT 204 62 " ALL QUESTIONS/STATEMENTS IN BOLD FACE REQUIRE WRITTEN RESPONSE" }{TEXT 220 2 ".)" }{TEXT 220 0 "" }}{PARA 221 "" 0 "" {TEXT 213 7 "ANSWER:" }{TEXT 213 0 "" }}{PARA 211 "" 0 "" {TEXT 250 41 "Continue with the fo llowing calculations:" }{TEXT 250 0 "" }}{PARA 228 "" 0 "" {TEXT 220 4 "3. " }{XPPEDIT 18 0 "(1/5)^2+2;" "6#,&*$)*&\"\"\"F'\"\"&!\"\"\"\"# F'F'F*F'" }{TEXT 220 1 " " }{TEXT 220 0 "" }}{EXCHG {PARA 232 "> " 0 " " {TEXT 223 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 44 "Note the effect of the next execution line. " }{TEXT 250 0 "" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{PARA 221 "" 0 "" {TEXT 213 15 "What did it do?" }{TEXT 213 0 "" }}{PARA 228 "" 0 "" {TEXT 220 4 "4. " }{XPPEDIT 18 0 "(13-7)/7;" "6#*&,&\"#8\"\"\"\"\"(! \"\"F&F'F(" }{TEXT 220 1 " " }{TEXT 220 2 " " }{TEXT 220 0 "" }} {EXCHG {PARA 232 "> " 0 "" {TEXT 223 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 30 "Again try the evalf() command." }{TEXT 250 0 "" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{PARA 228 "" 0 "" {TEXT 220 4 "5. " }{XPPEDIT 18 0 "(8^2-3^3)*(5-2 2)/(8-4^2);" "6#*(,&*$)\"\")\"\"#\"\"\"F)*$)\"\"$F,F)!\"\"F),&\"\"&F) \"#AF-F),&F'F)*$)\"\"%F(F)F-F-" }{TEXT 220 1 " " }{TEXT 220 0 "" }} {EXCHG {PARA 232 "> " 0 "" {TEXT 223 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 30 "Again try the evalf() command." }{TEXT 250 0 "" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{PARA 228 "" 0 "" {TEXT 220 4 "6. " }{XPPEDIT 18 0 "factorial(27)/ (factorial(10)*factorial(17));" "6#*&-%*factorialG6#\"#F\"\"\"*&-F%6# \"#5F(-F%6#\"# " 0 "" {TEXT 223 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 37 "Note how this compares with the next " }{TEXT 250 0 "" } }{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 16 "binomial(27,10);" } {MPLTEXT 1 211 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 43 "7. Try the MAP LE command binomial(100,50);" }{TEXT 250 0 "" }}{EXCHG {PARA 232 "> " 0 "" {TEXT 223 0 "" }}}{PARA 228 "" 0 "" {TEXT 220 38 "8. Compute the corresponding number " }{XPPEDIT 18 0 "factorial(100)/(factorial(50) *factorial(50));" "6#*&-%*factorialG6#\"$+\"\"\"\"*&-F%6#\"#]F(F*F(!\" \"" }{TEXT 220 1 " " }{TEXT 220 2 " ." }{TEXT 220 0 "" }}{EXCHG {PARA 232 "> " 0 "" {TEXT 223 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 1 " " } {TEXT 250 0 "" }}{PARA 228 "" 0 "" {TEXT 220 6 " " }{TEXT 204 120 "This expression is called the \"binomial coefficient\" and someti mes referred to as \"100 choose 50.\" Do you know why?" }{TEXT 220 0 "" }}{PARA 211 "" 0 "" {TEXT 250 143 "9. Execute the following comman d sequence and record any relevant observations about what the command s do, automatic features of MAPLE, etc. " }{TEXT 250 0 "" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 6 "1+2/3;" }{MPLTEXT 1 211 0 "" }}} {EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 12 "1/2+1/3+1/4; " }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 8 "2/(3*4);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 " > " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 11 "Digits:=50;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 10 "sqrt(1/8);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "ev alf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 12 "(2/3)*(6/7);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 11 "Digits:=10;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 10 "sqrt(2)/3;" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "ev alf(%);" }{MPLTEXT 1 211 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 7 " \+ " }{TEXT 250 0 "" }}{PARA 228 "" 0 "" {TEXT 220 10 " " } {TEXT 204 94 "If eval is short for \"evaluate\" what do you think the \+ \"f\" in the command evalf stands for?" }{TEXT 220 0 "" }}{PARA 211 "" 0 "" {TEXT 250 85 "10. Execute the following command sequence and ag ain record relevant observations. " }{TEXT 250 0 "" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 5 "200!;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 7 "200!+1;" }{MPLTEXT 1 211 0 "" }} }{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 7 "100!/2;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 5 "1/6!;" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "ev alf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 6 "10/6!;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 7 "100/6!;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 8 "1000/6!;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 6 "1/ 50!;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 8 "1/50!+1;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 12 "Digits:=100;" }{MPLTEXT 1 211 0 "" }}} {EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 15 "evalf(1/50!+1);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 11 "D igits:=10;" }{MPLTEXT 1 211 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 4 " \+ " }{TEXT 250 0 "" }}{PARA 228 "" 0 "" {TEXT 220 6 "11. " }{TEXT 204 62 "Explain the meaning of the term \"floating point arithmetic.\" " }{TEXT 220 0 "" }}{PARA 211 "" 0 "" {TEXT 250 80 "12. Execute the f ollowing command sequence and record any relevant observations" }{TEXT 250 0 "" }}{EXCHG {PARA 216 "> " 0 "" {MPLTEXT 1 217 28 "convert(.333 33333,fraction);" }{MPLTEXT 1 217 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 29 "convert(.333333333,fraction);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 30 "convert(.3333333333, fraction);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 30 "convert(.3333333335,fraction);" }{MPLTEXT 1 211 0 " " }}}{EXCHG {PARA 242 "> " 0 "" {XPPEDIT 19 1 "convert(sqrt(2), fracti on);" "6#-%(convertG6$-%%sqrtG6#\"\"#%)fractionG" }{MPLTEXT 1 259 1 " \+ " }{TEXT 255 0 "" }}}{EXCHG {PARA 243 "> " 0 "" {XPPEDIT 19 1 "convert (evalf(sqrt(2)), fraction);" "6#-%(convertG6$-%&evalfG6#-%%sqrtG6#\"\" #%)fractionG" }{MPLTEXT 1 259 1 " " }{TEXT 255 0 "" }}}{PARA 232 "" 0 "" {TEXT 223 0 "" }}{PARA 228 "" 0 "" {TEXT 220 5 "12. " }{TEXT 204 46 "This last response is very misleading. Why? " }{TEXT 220 0 "" }} {PARA 228 "" 0 "" {TEXT 220 58 "13. Experiment with several examples \+ to determine if the " }{TEXT 220 7 "command" }{TEXT 204 29 " convert(e xpression,fraction)" }{TEXT 220 72 " is an \"exact operation\" or som e sort of \"approximate operation.\" " }{TEXT 204 13 "Which is it? " }{TEXT 220 25 " Show your examples ." }{TEXT 220 0 "" }}{PARA 211 "" 0 "" {TEXT 250 24 "14. Continue as before." }{TEXT 250 0 "" }} {EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 3 "Pi;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 12 "Digits:=100;" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 10 "e valf(Pi);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 20 "convert(%,fraction);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 27 "convert(%%,fraction,exact);" } {MPLTEXT 1 211 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 126 " Change th e above number of digits to 10 and reexecute the last three commands. \+ Finally, change to 4 digits and reexecute." }{TEXT 250 0 "" }}{EXCHG {PARA 232 "> " 0 "" {TEXT 223 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 100 "15. Pi is the numerical quantity and pi is the Greek letter. The fo llowing sequence exploits this." }{TEXT 250 0 "" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 6 "pi=Pi;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 9 "evalf(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 211 10 "evalf(pi);" }{MPLTEXT 1 211 0 "" }}}{PARA 211 "" 0 "" {TEXT 250 132 "In this last command w e asked MAPLE to find a floating point evaluation to the Greek symbol \+ pi , not to the numerical expression Pi." }{TEXT 250 0 "" }}{PARA 200 "" 0 "" {TEXT 216 0 "" }}{PARA 236 "" 0 "" {TEXT 257 0 "" }}{PARA 215 "" 0 "" {TEXT 233 0 "" }}{PARA 218 "" 0 "" {TEXT 262 0 "" }}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }