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256 34 "Why a saddle is called a \"saddle\"?" }}{PARA 0 "" 0 "" {TEXT 
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{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r
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on of the " }{TEXT 257 15 "gradient vector" }{TEXT -1 15 " of a functi
on " }{XPPEDIT 18 0 "f(x,y);" "6#-%\"fG6$%\"xG%\"yG" }{TEXT -1 13 " at
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0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 32 "The following command plots the " }{TEXT 259 12 "level
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\"yG" }{TEXT -1 27 ", that is the solutions of " }{XPPEDIT 18 0 "f(x,y
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35.000000 29.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Cur
ve 12" "Curve 13" "Curve 14" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 138 "Notice that the gradient vector field \+
is orthogonal to the level curves. To see this better, in the next pic
ture we plot the two together." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "plot1:=gradplot(f(x,y),x=-3
..3,y=-3..3,arrows=thick):plot2:=contourplot(f(x,y),x=-3..3,y=-3..3,co
ntours=15):display(plot1,plot2,scaling=constrained);" }}{PARA 13 "" 1 
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