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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "To find the Jacobian matri
x of a set of differential equations given by" }}}{EXCHG {PARA 0 "" 0 
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yy::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
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{PARA 0 "" 0 "" {TEXT -1 46 "First write the equations as a vector as \+
below" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "v:=[f,g,h.....];" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Then use the Jacobian command s
hown below" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "J:=jacobian(v
,[x,y,z.....]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "eg For the dif
ferential equations" }}}{EXCHG {PARA 0 "" 0 "" {OLE 1 3588 1 "[xm]Br=W
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{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(li
nalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=6*x^2+4*x*y;" 
}{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g:=x+4*y+3
*y^2;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "v:=[
f,g];" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "J:=
jacobian(v,[x,y]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
103 "To get the value of the Jacobian matrix at a particular point sub
stitute in the coordinates as follows." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 23 "e.g. at the point (0,0)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "J00:=subs(x=0,y=0,evalm(J));" }}}}{MARK "9 0 0" 15 }
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