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0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 217 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 218 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {PSTYLE "" -1 215 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 1 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 219 "Times" 1 12 0 0 0 1 1 1 1 2 2 2 0 0 0 1 }{CSTYLE "" -1 220 "Times" 1 12 0 0 0 1 1 1 1 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 221 0 "" }}{PARA 209 "" 0 "" {TEXT 221 0 "" } {TEXT 207 0 "" }{TEXT 207 27 "Brief Introduction to Maple" }}{PARA 0 " " 0 "" {TEXT 222 0 "" }{TEXT 208 0 "" }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 0 "" }{TEXT 209 0 "" }{TEXT 210 88 "1. Be sure you have opened this Maple worksheet as a Maple 13 Wor ksheet, and save often" }{TEXT 211 0 "" }{TEXT 212 1 "." }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 222 0 "" }{TEXT 207 121 "2. If you ever need to add another command line, you can pul l down the \"Insert\" menu and click on \"Add Execution Group.\"" } {TEXT 207 0 "" }{TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}} {EXCHG {PARA 211 "" 0 "" {TEXT 222 0 "" }{TEXT 207 0 "" }{TEXT 207 25 "3. Maple as a Calculator." }{TEXT 207 0 "" }{TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 64 "First, remember that all Maple commands end with a semi-colom, ;" }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 104 "You may use Maple as a calculator. Just put your curso r anywhere on the following lines and hit return." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 6 "1 + 2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "3.4 * ( 3 + 4 ) / 2 - 16.5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 74 "Note , that to force a Maple to give you a numeric answer, you can use the " }{TEXT 213 5 "evalf" }{TEXT 222 9 " command." }{TEXT 214 0 "" }{TEXT 222 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf( sqrt(2) \+ );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "1 + 2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 74 "For convenience, you can refer to the la st result Maple calculated with a " }{TEXT 215 1 "%" }{TEXT 222 2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "% + 4;" }}}{EXCHG {PARA 212 "" 0 "" {TEXT 222 0 "" }{TEXT 207 0 "" }{TEXT 207 31 "5. Defining \+ functions in Maple." }{TEXT 207 0 "" }{TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 32 "Let's define a functio n, f(x) = " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\"), T ypesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\"x\", italic = \"t rue\", mathvariant = \"italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), superscriptshift = \"0\")), Typesetting:-mi(\"\"));" "-I %mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6#Q!F'-F# 6#-I%msupGF$6%-F,6%Q\"xF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I #mnGF$6$Q\"2F'/F;Q'normalF'/%1superscriptshiftGQ\"0F'F+" }{TEXT 222 3 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f:=x-> x^2;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 222 101 "Using incorrect syntax when defi ning a funciton in Maple is one of the most common mistakes in Maple." }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 213 "" 0 "" {TEXT 207 90 "No tice that the f(x) in mathematical notation is replaced by f := x - > in Maple syntax." }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 81 "To confirm that the definition of f(x) is correct, chec k it at a few values of x." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(-4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 154 "One thing to remember when writing a mathematical \+ expression is that when two terms are being multiplied, you must type \+ in the multiplication operator, *." }}{PARA 0 "" 0 "" {TEXT 222 0 "" } }{PARA 0 "" 0 "" {TEXT 222 26 "So, try to define g(x) = 3" }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Types etting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \+ \"italic\"), Typesetting:-mn(\"2\", mathvariant = \"normal\"), supersc riptshift = \"0\")), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6#Q!F'-F#6#-I%msupGF$6%-F,6%Q \"xF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#mnGF$6$Q\"2F'/F;Q'n ormalF'/%1superscriptshiftGQ\"0F'F+" }{TEXT 222 19 " correctly in Mapl e" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 48 "Evaluate the function g(x) at three values of x." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 214 "" 0 "" {TEXT 222 0 "" }{TEXT 207 0 "" }{TEXT 207 13 "6. For-loops" }{TEXT 207 0 "" }{TEXT 207 1 "." }{TEXT 207 0 "" } {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 171 "One of the classic structures in a programming language is the \"for-loop.\" In Maple, we will use a \"for-loop\" to generat e several function values. Note that we will use " }{TEXT 216 0 "" } {TEXT 217 1 "i" }{TEXT 218 0 "" }{TEXT 222 154 " as the loop-control o r \"dummy\" variable. Below, the loop calculates f(0), f(1), ... , f( 10), and prints this value along with the loop-control variable." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for i from 0 to 10 do\n" } {MPLTEXT 1 0 19 " print (i,f(i));\n" }{MPLTEXT 1 0 7 "end do;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 222 53 "Write a similar loop to print g(0 ), g(1), ..., g(10)." }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 83 "If you want to continue a line, without hitting \"ent er,\" you can hit \"shift-enter.\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 215 "" 0 "" {TEXT 222 0 "" }{TEXT 207 0 "" }{TEXT 207 31 "7. Sequences stored in arrays." }{TEXT 207 0 "" }{TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 84 "Now, consider the sequence we discussed in class for the number of edges of n boxes." }}{PARA 0 "" 0 "" {TEXT 222 21 "4, 7, 10 , 13, 16, ..." }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 4 "The " }{TEXT 219 11 "closed form" }{TEXT 222 23 " for thi s sequence was " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mfence d(Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Typesetti ng:-msub(Typesetting:-mi(\"a\", italic = \"true\", mathvariant = \"ita lic\"), Typesetting:-mrow(Typesetting:-mi(\"n\", italic = \"true\", ma thvariant = \"italic\")), subscriptshift = \"0\"), Typesetting:-mo(\"= \", mathvariant = \"normal\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mrow(Typesetting:-mi(\"\"), T ypesetting:-mrow(Typesetting:-mn(\"3\", mathvariant = \"normal\"), Typ esetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \+ \"false\", separator = \"false\", stretchy = \"false\", symmetric = \" false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"n\", italic = \"true\", mathvariant = \"italic\")), Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", s tretchy = \"false\", symmetric = \"false\", largeop = \"false\", movab lelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rs pace = \"0.2222222em\"), Typesetting:-mn(\"1\", mathvariant = \"normal \")), Typesetting:-mi(\"\")), Typesetting:-mi(\"\")), mathvariant = \" normal\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#- I(mfencedGF$6$-F#6%-I#miGF$6#Q!F'-F#6&-I%msubGF$6%-F16%Q\"aF'/%'italic GQ%trueF'/%,mathvariantGQ'italicF'-F#6#-F16%Q\"nF'F/%)stretchyGF>/%*symme tricGF>/%(largeopGF>/%.movablelimitsGF>/%'accentGF>/%'lspaceGQ,0.27777 78emF'/%'rspaceGFM-F,6%Q\"nF'/%'italicGQ%trueF'/F6Q'italicF'F+" }{TEXT 222 3 " ." }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 66 "The for-loop below will print the first 10 terms of this seque nce." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for n from 1 to 10 \+ do\n" }{MPLTEXT 1 0 19 " print(n,3*n+1);\n" }{MPLTEXT 1 0 7 "end do; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 92 "Maple also allows you to sto re the values of the sequence in an array, as in the code below." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a:=array(1..10);\n" } {MPLTEXT 1 0 22 "for n from 1 to 10 do\n" }{MPLTEXT 1 0 20 " a[n] := 3*n + 1;\n" }{MPLTEXT 1 0 7 "end do;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 47 "Now we can display a few values of the array a." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[5];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[6 ];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 222 22 "Finally, consider the " } {TEXT 220 11 "recursively" }{TEXT 222 18 " defined sequence " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-m row(Typesetting:-msub(Typesetting:-mi(\"b\", italic = \"true\", mathva riant = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"n\", italic = \"true\", mathvariant = \"italic\")), subscriptshift = \"0\"), Typese tting:-mo(\"=\", mathvariant = \"normal\", fence = \"false\", separato r = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0 .2777778em\", rspace = \"0.2777778em\"), Typesetting:-mrow(Typesetting :-msub(Typesetting:-mi(\"b\", italic = \"true\", mathvariant = \"itali c\"), Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Types etting:-mi(\"n\", italic = \"true\", mathvariant = \"italic\"), Typese tting:-mo(\"−\", mathvariant = \"normal\", fence = \"false\", se parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn(\"1\", \+ mathvariant = \"normal\")), Typesetting:-mi(\"\")), subscriptshift = \+ \"0\"), Typesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"fal se\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mn (\"4\", mathvariant = \"normal\")), Typesetting:-mi(\"\")), Typesettin g:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 %-I#miGF$6#Q!F'-F#6&-I%msubGF$6%-F,6%Q\"bF'/%'italicGQ%trueF'/%,mathva riantGQ'italicF'-F#6#-F,6%Q\"nF'F7F:/%/subscriptshiftGQ\"0F'-I#moGF$6- Q\"=F'/F;Q'normalF'/%&fenceGQ&falseF'/%*separatorGFM/%)stretchyGFM/%*s ymmetricGFM/%(largeopGFM/%.movablelimitsGFM/%'accentGFM/%'lspaceGQ,0.2 777778emF'/%'rspaceGFfn-F#6%-F26%F4-F#6%F+-F#6%F?-FF6-Q(−F'FIFKF NFPFRFTFVFX/FenQ,0.2222222emF'/FhnFeo-I#mnGF$6$Q\"1F'FIF+FB-FF6-Q\"+F' FIFKFNFPFRFTFVFXFdoFfo-Fho6$Q\"4F'FIF+F+" }{TEXT 222 9 " , where " } {XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-m row(Typesetting:-msub(Typesetting:-mi(\"b\", italic = \"true\", mathva riant = \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"1\", mathvari ant = \"normal\")), subscriptshift = \"0\"), Typesetting:-mo(\"=\", ma thvariant = \"normal\", fence = \"false\", separator = \"false\", stre tchy = \"false\", symmetric = \"false\", largeop = \"false\", movablel imits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspac e = \"0.2777778em\"), Typesetting:-mn(\"5\", mathvariant = \"normal\") ), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingG I(_syslibGF'6%-I#miGF$6#Q!F'-F#6%-I%msubGF$6%-F,6%Q\"bF'/%'italicGQ%tr ueF'/%,mathvariantGQ'italicF'-F#6#-I#mnGF$6$Q\"1F'/F;Q'normalF'/%/subs criptshiftGQ\"0F'-I#moGF$6-Q\"=F'FC/%&fenceGQ&falseF'/%*separatorGFN/% )stretchyGFN/%*symmetricGFN/%(largeopGFN/%.movablelimitsGFN/%'accentGF N/%'lspaceGQ,0.2777778emF'/%'rspaceGFgn-F@6$Q\"5F'FCF+" }{TEXT 222 2 " ." }}{PARA 0 "" 0 "" {TEXT 222 0 "" }}{PARA 0 "" 0 "" {TEXT 222 90 "F ill in the code below, which fills an array \"b\" with the first 10 te rms of this sequence." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "b: =array(1..10);\n" }{MPLTEXT 1 0 12 "b[1]:= \n" }{MPLTEXT 1 0 22 "f or n from 2 to 10 do\n" }{MPLTEXT 1 0 27 " b[ ] := b[n-1] + ;\n " }{MPLTEXT 1 0 7 "end do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }