{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 3 1}{FONT 0 "-adobe-helve
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lvetica-Bold" 12}{FONT 1 "-adobe-times-medium-r-normal--14-*" "ti
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12}{FONT 3 "-adobe-new century schoolbook-bold-r-normal--17-*" "n
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 4 "-adobe-new century schoolbook-bold-r-normal--17-*" "new centu
ry schoolbook" "Times-Bold" 8 17 64 "Times-Bold" 17}{SCP_R 1 0 25
{COM_R 2 0{TEXT 4 29 "\015Maple in Science Education.\015"}}
{COM_R 3 0{TEXT 1 84 "Statistical Mechanics: Maxwell Gas\012Darre
n Redfern, Tony Scott, Richard Pavelle\011\011\011\011\011\015"}}
{COM_R 4 0{TEXT 1 64 "Find the most probable speed of a Maxwell-B
otzman Distribution.\015"}}{INP_R 5 0 "> "{TEXT 0 68 "n := v -> 4
*Pi*(n.o)*((m/(2*Pi*k*T))^(3/2))*exp(-m*v^2/(2*k*T))*v^2:"}}
{INP_R 6 0 "> "{TEXT 0 5 "n(v);"}}{OUT_R 7 0 6{DAG *11n3\`Pi`/3i2
x0001j2x0002n3\`no`j2x0001p6/3pAp6n3\`m`/3j2x0003p6n3\`k`/3i2x000
3p6n3\`T`p18(3n3\`exp`,2+3*9p10pAn3\`v`p6p16p4p1Cp4p3pAp27p6}}
{COM_R 8 0{TEXT 1 86 "The value v such that n(v) is maximized wil
l be a point where the derivative is zero.\015"}}{INP_R 9 0 "> "
{TEXT 0 19 "dv := diff(n(v),v):"}}{INP_R 10 0 "> "{TEXT 0 28 "Cri
tPoints := solve(dv=0,v);"}}{OUT_R 11 0 10{DAG :3n5\`CritPoints`,
4j2x0000*9n3\`m`/3i2x0001j2x0002pE/3j2x0001pEn3\`k`p11n3\`T`p11+3
p8pC}}{COM_R 12 0{TEXT 1 82 "Since the speed v is by definition a
 magnitude, the negative result is discarded.\015"}}{INP_R 13 0 "
> "{TEXT 0 70 "CritPoints := select(t -> evalb(signum(op(1,t)) <>
 -1), [CritPoints]);"}}{OUT_R 14 0 13{DAG :3n5\`CritPoints`[2,3j2
x0000*9n3\`m`/3i2x0001j2x0002pF/3j2x0001pFn3\`k`p12n3\`T`p12}}
{COM_R 15 0{TEXT 1 58 "Find the point of maximum via the second d
erivative test.\015"}}{INP_R 16 0 "> "{TEXT 0 20 "for i from 1 to
 2 do"}}{INP_R 17 0 "> "{TEXT 0 61 "    test.i := simplify(subs(v
=CritPoints[i],diff(n(v),v$2))):"}}{INP_R 18 0 "> "{TEXT 0 3 "od;
"}}{OUT_R 19 0 18{DAG :3n4\`test1`+3*Dn3\`Pi`/3i2x0001j2x0002n3\`
no`j2x0001pB/3pFpBn3\`m`/3j2x0003pBn3\`k`/3i2x0003pBn3\`T`p1DpB}}
{OUT_R 20 0 18{DAG :3n4\`test2`+3*Fn3\`Pi`/3i2x0001j2x0002n3\`no`
j2x0001pB/3pFpBn3\`m`/3j2x0003pBn3\`k`/3i2x0003pBn3\`T`p1D(3n3\`e
xp`,2p9pFi2x0004}}{COM_R 21 0{TEXT 1 93 "The point where the seco
nd derivative is negative is the point of maximum, the rms veloci
ty.\015"}}{INP_R 22 0 "> "{TEXT 0 54 "if signum(op(1,test1)) = -1
 then maxv := CritPoints[1]"}}{INP_R 23 0 "> "{TEXT 0 56 "elif si
gnum(op(1,test2)) = -1 then maxv := CritPoints[2]"}}{INP_R 24 0 "
> "{TEXT 0 3 "fi;"}}{OUT_R 25 0 24{DAG :3n4\`maxv`*9n3\`m`/3i2x00
01j2x0002pA/3j2x0001pAn3\`k`pDn3\`T`pD}}{INP_R 26 0 "> "{TEXT 0 0
 ""}}}{END}
