{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "Courie r" 0 1 0 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 "" 0 258 1 {CSTYLE "" -1 -1 "Courier" 0 1 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "In-class project" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 58 "1. Cha pter 2, problem 6(a), the Brent-Salamin Algorithm " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "2. Chapter 3, problem 10 , Vector projection" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 43 "3. Write a program that, for input number " }{XPPEDIT 18 0 "s;" "6#%\"sG" }{TEXT -1 80 ", adds random numbers in [0.0, 1.0] until the sum is larger than or equals to " }{XPPEDIT 18 0 "s;" "6#% \"sG" }{TEXT -1 166 " and outputs the number of terms added. Genera te a 10000-dimensional vector of such random numbers for the experimen t inside your program. A while-do is required." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "4. Extra credit problem: Chapter 2, Problem 28 (Nested sum II)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 86 "Answers (except the extra credit p roblem) will be available on my website later today." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 258 53 "Chapter 2, problem 6(a), the Brent-Salamin Algorithm" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }} {PARA 256 "" 0 "" {TEXT -1 325 "BrentSalamin := proc( n )\n local a, b, t, p, k;\n\n a[0], b[0], t[0], p[0] := 1, 1/sqrt(2), 1/4, 1;\n \+ for k from 0 to n-1 do\n a[k+1] := (a[k]+b[k])/2;\n b[k+1] \+ := sqrt(a[k]*b[k]);\n t[k+1] := t[k] - (a[k]-a[k+1])^2 * p[k];\n \+ p[k+1] := 2*p[k];\n end do;\n\n return evalf((a[n]+b[n])^2/(4 *t[n]));\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "read(\"c:/aaa/teach/340/Fall08/BrentSalamin .mpl\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Digits := 50:\n BrentSalamin(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"S]P*Rpr>%)G]zKQ VEYQKz*e`EfTJ!#\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf( Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"S^P*Rpr>%)G]zKQVEYQKz*e`EfT J!#\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 259 42 " Chapter 3, problem 10, \+ Vector projection" }}{PARA 257 "" 0 "" {TEXT -1 720 "VectorProject := proc( x, y )\n local n, z, alpha, s, t, k;\n\n n := LinearAlgebra [Dimension](x); # get dimension n\n \n s := 0; \+ # compute the sum\n for k from 1 to n do # in the numerator\n s := s + x[k]*y[k]; # of alpha\n e nd do;\n\n t := 0; # compute the sum\n \+ for k from 1 to n do # in the denominator\n t := t \+ + y[k]^2; # of alpha\n end do;\n\n alpha := s/t; \+ # get alpha\n\n z := Vector[row](n); \+ # intialize z as empty vector\n for k from 1 to n do \n z[ k] := alpha*y[k]; # assign values in z\n end do;\n\n \+ return evalf(z);\nend proc;" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "read(\"c:/aaa/teach/ 340/Fall08/VectorProject.mpl\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "x := LinearAlgebra[RandomVector][row](6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'RTABLEG6%\"*))GWZ\"-%'VECTORG6#7(\" #x\"\"*\"#J!#]!#!)\"#V&%'VectorG6#%$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "y := LinearAlgebra[RandomVector][row](6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG-%'RTABLEG6%\"*GHWZ\"-%'VECTORG6#7(\"# C\"#l\"#')\"#?!#h!#[&%'VectorG6#%$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "z := VectorProject(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG-%'RTABLEG6%\"*3IWZ\"-%'VECTORG6#7($\"+B&R?\"*)! \"*$\"+rtn8C!\")$\"+H3[$>$F2$\"+.'*pEuF/$!+zL9lAF2$!+0zS#y\"F2&%'Vecto rG6#%$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 11 " Problem 3" }}{PARA 258 "" 0 "" {TEXT -1 349 "RandomAdd := proc( s )\n local a, t, k;\n \n # generate \+ random numbers\n a := LinearAlgebra[RandomVector](10000,generator=0. 0..1.0);\n\n t := 0; # initialize the sum\n k := 0; # initiali ze the counter\n while t < s do\n k := k + 1; # update the count\n t := t + a[k]; # add a random number\n end do;\n\n \+ return k;\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "read(\"c:/aaa/teach/340/Fall08/RandomAdd. mpl\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "RandomAdd(100); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$8#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}}{MARK "2 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 147442888 147442928 147443008 }{RTABLE M7R0 I6RTABLE_SAVE/147442888X*%)anythingG6"6"[gl!$%!!!"'"'"#x""*"#J!#]!#!)"#VF& } {RTABLE M7R0 I6RTABLE_SAVE/147442928X*%)anythingG6"6"[gl!$%!!!"'"'"#C"#l"#')"#?!#h!#[F& } {RTABLE M7R0 I6RTABLE_SAVE/147443008X*%)anythingG6"6"[gl!$%!!!"'"'$"+B&R?"*)!"*$"+rtn8C!")$" +H3[$>$F,$"+.'*pEuF)$!+zL9lAF,$!+0zS#y"F,F& }