{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 }{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 "Norma
l" -1 256 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" -1 257 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" -1 258 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 "Normal" -1 
259 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 "" 259 260 1 {CSTYLE "" -1 -1 "" 0 1 
0 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 256 "" 0 "" {TEXT -1 39 "Gradient Vector Fields a
nd Level Curves" }}{PARA 0 "" 0 "" {TEXT -1 11 "Objectives:" }}{PARA 
0 "" 0 "" {TEXT -1 143 "(1) If f(x,y) represents the height above the \+
sea level at a point with coordinate (x,y). We observe that the gradie
nt vectors point \"uphill'. " }}{PARA 0 "" 0 "" {TEXT -1 71 "(2) The g
raident vector is perpendicular to the level curve at a point." }}
{PARA 0 "" 0 "" {TEXT -1 123 "(3) A curve of steepest ascent (to the t
op of the hill) can be drawn out of the gradient vector fields and the
 level curve." }}{PARA 0 "" 0 "" {TEXT -1 10 "Example 1." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 32 "plot3d(x^2+y^2,x=-2..2,y=-2..2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "contourplot(x^2+y^2,x=-2..2,y=-2..2
,contours=30,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 76 "plot1:=contourplot(x^2+y^2,x=-2..2,y=-2..2,contours=3
0,scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "
plot2:=gradplot(x^2+y^2,x=-2..2,y=-2..2,scaling=constrained,arrows=sli
m):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "display(plot1,plot2)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 258 "
" 0 "" {TEXT -1 10 "Example 2." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plo
t3d(20-4*x^2-y^2,x=-3..3,y=-5..5);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "contourplot(20-4*x^2-y^2,x=-3..3,y=-5..5,contours=30,
scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "pl
ot1:=contourplot(20-4*x^2-y^2,x=-3..3,y=-5..5,contours=30,scaling=cons
trained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "plot2:=gradplo
t(20-4*x^2-y^2,x=-3..3,y=-5..5,scaling=constrained,arrows=slim):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "display(plot1,plot2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 260 "" 0 "
" {TEXT -1 10 "Example 3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot3d(
x^2-y^2,x=-3..3,y=-5..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
69 "contourplot(x^2-y^2,x=-5..5,y=-5..5,contours=30,scaling=constraine
d);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "plot1:=contourplot(x
^2-y^2,x=-5..5,y=-5..5,contours=30,scaling=constrained):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "plot2:=gradplot(x^2-y^2,x=-5..5,y=-
5..5,scaling=constrained,arrows=slim):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "display(plot1,plot2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 4 0" 55 }{VIEWOPTS 
1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }