{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 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 "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "Module 11 : Multivariable Calcul us" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 30 "110 1 : Multivariable Functions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 9 "S E T U P" }} {PARA 0 "" 0 "" {TEXT -1 252 "In this project we will use the followin g command packages. Type and execute this line before begining the pro ject below. If you re-enter the worksheet for this project, be sure to re-execute this statement before jumping to any point in the workshee t." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart; with(plots):" }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "_____________________________________________________________________ ______________" }}{PARA 4 "" 0 "" {TEXT -1 35 "A. Define a Funciton of 2 Variables" }}{PARA 0 "" 0 "" {TEXT -1 83 "_________________________ __________________________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Note that you can evaluate the function with...." }}{PARA 0 "" 0 "" {TEXT -1 59 "number s, variables, or expressions which can be simplified." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f := (x,y ) -> x/ (x^2 + y^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6$%\"xG %\"yG6\"6$%)operatorG%&arrowGF)*&9$\"\"\",&*$)F.\"\"#F/F/*$)9%F3F/F/! \"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(1,2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(2,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"# \"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f(-3,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(1/2,1/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#= \"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f(A, -1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"AG\"\"\",&*$)F$\"\"#F%F%F%F%!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(a,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"aG\"\"\",&*$)F$\"\"#F%F%*$)%\"bGF)F%F%!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(b,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"bG\"\"\",&*$)%\"aG\"\"#F%F%*$)F$F*F%F%!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f( r +1, s-1);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#*&,&%\"rG\"\"\"F&F&F&,&*$)F$\"\"#F&F&*$),&%\"sGF &F&!\"\"F*F&F&F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplif y(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"rG\"\"\"F&F&F&,,*$)F% \"\"#F&F&*&F*F&F%F&F&F*F&*$)%\"sGF*F&F&*&F*F&F.F&!\"\"F0" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "_________________________________________________________ __________________________" }}{PARA 4 "" 0 "" {TEXT -1 34 "B. Graph a \+ function of 2 Variables" }}{PARA 0 "" 0 "" {TEXT -1 83 "______________ _____________________________________________________________________ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 54 "A basic three dimensional graph is accomp lished by the" }{TEXT 256 7 " plot3d" }{TEXT -1 9 " command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "Note that you n eed to specify three items : the function, the x domain, and the y dom ain." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "plot3d( x^2 + y^2 - x*y^2 + y*x^2, x = -3..3, y = -3. .3);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6$-%%GRIDG 6%;$!\"$\"\"!$\"\"$F)F&X,%)anythingG6\"6\"][[[[]\\q\\bm\":\":403200000 0000000402D00000000000040270000000000004022000000000000401C00000000000 0401600000000000040120000000000004010000000000000401000000000000040120 000000000004016000000000000401C000000000000402200000000000040270000000 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