{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "N ormal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 16 "Can Maple Solve " }} {PARA 18 "" 0 "" {TEXT -1 30 "Simple Differential Equations?" }}{PARA 19 "" 0 "" {TEXT -1 21 "Math 374 Fall 1999" }}{PARA 19 "" 0 "" {TEXT -1 11 "Jay Treiman" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Maple has a collection of procedures and functions" }}{PARA 0 "" 0 "" {TEXT -1 51 "that will solve many differential equations. These" }} {PARA 0 "" 0 "" {TEXT -1 55 "routines can plot numerical solutions and slope fields," }}{PARA 0 "" 0 "" {TEXT -1 59 "find numerical solution s, and find exact solutions to some " }}{PARA 0 "" 0 "" {TEXT -1 23 "d ifferential equations." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "In this worksheet you will test Maple's ability to s olve" }}{PARA 0 "" 0 "" {TEXT -1 57 "some simple differential equation s from the first chapter" }}{PARA 0 "" 0 "" {TEXT -1 12 "of the text. " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Restart" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "It is always a good idea to restart." }{TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " restart;" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 "Using dsolve." }} {PARA 0 "" 0 "" {TEXT -1 12 "The routine " }{HYPERLNK 17 "dsolve" 2 "d solve" "" }{TEXT -1 37 " is Maple's basic routine for solving" }} {PARA 0 "" 0 "" {TEXT -1 56 "differential equations. You have already seen how it is" }}{PARA 0 "" 0 "" {TEXT -1 50 "used if you have gone \+ through the first worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "Here is the solution to the logistic growth exa mple" }}{PARA 0 "" 0 "" {TEXT -1 53 "from the text (see Page 43 or Pag e 77 of Edwards and " }}{PARA 0 "" 0 "" {TEXT -1 10 "Penney). " }} {PARA 0 "" 0 "" {TEXT -1 17 "Remember to make " }{XPPEDIT 18 0 "N;" "6 #%\"NG" }{TEXT -1 15 " a function of " }{XPPEDIT 18 0 "t;" "6#%\"tG" } {TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "de1 := diff(N(t),t)=k*N(t)-k1*N(t)^2;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(de1,N(t));" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "One can put num bers in for the constants and" }}{PARA 0 "" 0 "" {TEXT -1 58 "solve an initial value problem. The graph of the function" }}{PARA 0 "" 0 "" {TEXT -1 20 "is what one expects." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "de2 := subs(\{k=1,k1=.005\} ,de1);\nsoln_de2 := dsolve(\{de2,N(0)=100\},N(t));\nplot(rhs(soln_de2) ,t=0..25);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "By using the " }{HYPERLNK 17 "infolevel" 2 "infolevel" "" } {TEXT -1 22 " command, one can get " }}{PARA 0 "" 0 "" {TEXT -1 41 "in formation on what technique Maple uses." }}{PARA 0 "" 0 "" {TEXT -1 27 "The default infolevel is 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "infolevel[dsolve] := 3;\nsol n_de2 := dsolve(\{de2,N(0)=100\},N(t));\ninfolevel[dsolve] := 1:" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Exercises" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 49 "Test Maple's ability to solve simple differential" }} {PARA 0 "" 0 "" {TEXT -1 48 "equation on problems 10, 15, 19, 20, 23, \+ 26, and" }}{PARA 0 "" 0 "" {TEXT -1 45 "30 from the Chapter 1 Review P roblems on page" }}{PARA 0 "" 0 "" {TEXT -1 26 "74 of Edwards and Pen ney." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Check which technique Map le uses for problems" }}{PARA 0 "" 0 "" {TEXT -1 51 "1, 5, and 23 from the Chapter 1 Review Problems on " }}{PARA 0 "" 0 "" {TEXT -1 44 "pag e 74 of Edwards and Penney. Explain why" }}{PARA 0 "" 0 "" {TEXT -1 46 "you would or would not use the technique Maple" }}{PARA 0 "" 0 "" {TEXT -1 5 "uses." }}}}}{MARK "2" 0 }{VIEWOPTS 1 1 0 1 1 1803 }