{VERSION 3 0 "IBM INTEL NT" "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 "" -1 256 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -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 "M aple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 0 "" }{TEXT 258 50 "THREE-DIMENSIONAL GRAPHS---RECTANGULAR COORDINATES" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 0 "" }{TEXT 261 0 "" }{TEXT 265 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "We have to start by loadi ng our 'plots' packages:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT 256 28 "Functions Defined Explicitly" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "A function defined explicitly i n two variables usually has the form:" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 48 " \+ f(x, y) = " }{TEXT 267 24 "an expression in x and y" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "or" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 42 " \+ z = " }{TEXT 268 25 "an expression in x and y." }{TEXT 269 0 "" }{TEXT 270 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 148 "We use the 'plot3d' command instead \+ of the 'plot' command to graph these functions. The syntax is similar to the syntax used in the 'plot' command:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 " plot3d (" }{TEXT 271 12 "expression, " }{TEXT -1 4 "x = " }{TEXT 272 11 "lowe r limit" }{TEXT -1 4 " .. " }{TEXT 273 13 "upper limit, " }{TEXT -1 4 "y = " }{TEXT 274 12 "lower limit " }{TEXT -1 3 ".. " }{TEXT 275 11 "u pper limit" }{TEXT -1 2 ");" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 279 266 "Plotting graphs in three dimen sions on Maple can be confusing because of the way Maple labels the co ordinate axes. I recommend using different ranges for x, y, and z on \+ the coordinate axes so that you can tell the difference. Ignore the l abels on the Maple output." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "Let's try graphing:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 " f (x, y) = y^2 - x^2" }}{PARA 0 "" 0 "" {TEXT -1 46 " \+ x = -10 to 10" }}{PARA 0 "" 0 "" {TEXT -1 46 " \+ y = -15 to 15" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot3d(y^2-x^2,x=-10..10, y=-15..15);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 211 "Uh oh--no axes! We ha ve to tell Maple that we want to see the axes by including an 'axes' c ommand in the 'plot3d' command. We may use either 'axes=normal' or 'a xes=boxed'. Try them both to see the difference:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot3d(y^2- x^2,x=-10..10,y=-15..15,axes=normal);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 408 "Now for something really cool--click on the graph. You'll see a box drawn around the picture. You can now move the mouse around (hold down the left mouse button) \+ and see the graph from different perspectives. (Notice how the x, y, \+ and z labels on the axes don't always keep up with the appropriate axe s--that's why I recommend using different axes lengths so that you can easily tell which axis is which.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 280 0 "" }{TEXT 281 0 "" }{TEXT 282 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 283 0 "" }{TEXT 284 0 "" } {TEXT 285 28 "Functions Defined Implicitly" }{TEXT 286 0 "" }{TEXT 287 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 250 "A function in three variables defined implicitly (i e, as an equation in three variables) will graph as a three-dimensiona l graph. We use 'implicitplot3d' to graph these functions. The synta x is similar to the 'implicitplot' command we used earlier." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Suppose we want to graph:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 57 " x^2 + 20 y^2 + 45 z^2 = 500." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "We can us e the following:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "implicitplot3d(x^2+20*y^2+45*z^2=500,x=-25..2 5,y=-20..20,z=-15..15,axes=normal);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 92 "OK--the graph looks kind of \"boxy.\" What can we do? One thing we \+ can try is the following:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "implicitplot3d(x^2+20*y^2+45*z^2=50 0,x=-25..25,y=-20..20,z=-15..15,axes=normal,grid=[18,18,18]);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 327 "T he 'grid' command changes the \"resolution\" of the picture--you can g et more detail (or less detail) by changing the numbers in the 'grid' \+ command. Note: If you change the numbers in the 'grid' command, you \+ are changing the number of points Maple is plotting, which may mean th at Maple will take longer to graph the function." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "10 2 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }