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{SECT 0 {PARA 256 "" 0 "" {MPLTEXT 0 21 0 "" }}{PARA 257 "" 0 "" 
{TEXT 256 41 "Calculus Lab 5\nSpace curves and curvature" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 53 "Here we wi
ll use the linear algebra package of Maple." }}{PARA 3 "" 0 "" {TEXT 
-1 16 "To load it, type" }{TEXT 257 13 " with(linalg)" }{TEXT -1 44 ":
 \nThe calling sequence of a space curve is\n" }{TEXT 258 28 "F:=vecto
r([f(t),g(t),h(t)]);" }{TEXT -1 88 " where f,g,h are expressions\nin t
he variable t. Define the space curve with coordinates\n" }{TEXT 259 
12 "t,t^2,sin(t)" }{TEXT -1 2 " ." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 1 "?" }}}{PARA 0 "" 0 "" {TEXT 260 26 "To plot a spacecur
ve type " }{TEXT 261 33 "spacecurve(op(F),t=a..b,options);" }{TEXT 
262 123 "\nThe options can include: thickness=2, axes=boxed, color=blu
e, labels=[x,y,z], etc. First load the plots package by typing " }
{TEXT 272 13 "with(plots): " }{TEXT 270 102 "With the cursor in the gr
aphic window, hold down the right mouse button, and try various plot o
ptions." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 75 "The derivatives of the components of a sp
ace curve\nis given by the command " }{TEXT 263 16 "map(diff, F,t): " 
}{TEXT -1 55 "you can also\nasign a name for this space curve such as \+
" }{TEXT 264 3 "G:=" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}
{SECT 0 {PARA 4 "" 0 "" {TEXT -1 28 "The length of F is given by\n" }
{TEXT 265 11 "norm(G,2); " }{TEXT -1 59 "work out the length of  G and
\nassign the variable N to it: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 1 "?" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "
" {TEXT -1 63 "Work out the arc length of F between a and b using\nthe
 command " }{TEXT 266 22 "evalf(Int(N,t=a..b)); " }{TEXT -1 36 "What i
s this length between 0 and 1?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 1 "?" }}}{PARA 258 "" 0 "" {TEXT -1 169 "What does Int do alone and \+
what is the role of the evalf command?\n..............................
......................................................................
..." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 53 "Find the unit tangent vec
tor to F, using the command\n" }{TEXT 267 13 "normalize(G);" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 
-1 115 "Find the curvature for F.  First define H as the second deriva
tive of F, then use the crossproduct (the command is " }{TEXT 268 15 "
crossprod(G,H);" }{TEXT -1 1 ")" }{TEXT 269 2 "  " }{TEXT -1 31 "then \+
use the curvature formula." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 
"?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 1 "?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
1 "?" }}}}{PARA 0 "" 0 "" {TEXT 271 142 "Print the entire worksheet wi
th your name inserted.\nTo get the graphic in the worksheet, choose fr
om the\nOptions Plot Display and then Inline." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{MARK "4 2 1 0 0" 1 
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