概要信息：

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2.1 Ôn¢ÚÿþØ
ÿþØ=ÿþŠ−ýŠ
2.1.1 XÚØ
õgÿþژÔnþ§ÿþŠéýŠ l´ƒÓ§5
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1. ¤L": £
2. nØúªCq5
3. ¤ì(Ø
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5. ÿþö)n%nσK
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§Ì‡´‚éäN¯KäN©Û.
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1
2.1.2 ‘ÅØ
duó,!Ø(½σE¤z˜gÿþŠÃ5ÆÞá§Ã{ÏLþ˜gÿþŠýOe
˜gÿþŠŒù˜aØ‘ÅØ.5
Œ—):
1. ÚOÞá
2. ‚¸^‡Ø(½5
3. ÿþþgØ(½5
ÙA:3u‘Å5§3ƒÓ÷*^‡e§é,˜Ônþ?1õgÿþ§Œ±uyÙÿþŠÑ
l,«VÇ©Ù. Œõê‘ÅØÑl©Ùµ
ρ(x) =
1√
2πσ
e−x
2/2σ2
Ï"E(x) = 0§D(x) = σ2.
Ødƒ	„kÑlþ!©Ù‘Åص
ρ(x) =

1
2e , −e ≤ x ≤ e
0, x < −ex > e
Ï"E(x) = 0§D(x) = e2
3 .
2.2 ÿþ(JØ(½Ý

Oÿþ(JŒ‚§Ý§·‚rÿþ(J
Y = N ±∆N
/ª§L«ÿþ±˜½VÇ£¡˜&VǤá3«m[N −∆N,N + ∆N ] ¥§∆N´é
ÿþØŒUêŠÿݧ´é‘ÿþýŠŒU3‰ŒO§Ï~Œ±ÀJ˜&V
Ç100%4Ø(½Ýe½IO󧽽´IOêcσ.
2.2.1 †ÿþ(JØ(½ÝO
ÿ˜gŒ±^¤ì#ŠØ(½Ý½ÓžŠâ¢S¢^‡O˜‡4Ø(½Ý.4Ø
†IO†ŽŒ±^þ!©Ù.?n§=
e =
√
3σ
ƒÓ^‡eõgÿþ‡^²þŠ“LÿþZŠ§ÙØ(½Ýdlúª‰Ñ
σN̄ =
σN√
n
=
√∑n
i=1(Ni − N̄)2
n(n− 1)
2
2.2.2 mÿþ(JØ(½ÝO
emÿþŠN´s‡pƒÕá†ÿþþx1, x2..., xs¼ê
N = f(x1, x2, ..., xs)
Øž§ŠâV?êúªŒò‡†ÿþ(JØ(½ÝÜ¡mÿþ(JØ(
½Ý§Ï~¦^ÚŠÜ¤.e^σx1 , σx2 , ..., σxsL«x1, x2..., xsIO§KNIOσNd
e¡úª‰Ñ.
σN =
√√√√ s∑
i=1
(
∂f
∂xi
σxi)
2
2.3 kêi,êŠÖÚ$Ž5K
du?ÛÔnþÿþ(Jѝ¹Ø§ÏdÙêŠATm©kؘü §ùpÑ
˜ §±êiUìoÊ\½öo8\Ênó5K.ù´˜«oчAØ(½
ÝL«{.
kêi êk†>1˜‡Ø´"êm©Žåm>ê1 ½1n Ž.
Ö˜„‡†Ø(½Ý˜ Ï~´=k˜ à§êŠéŒ½éžæ^‰ÆEâ
{L«.
kêi$Ž÷v˜e5K:
1. \~a.§" †ŒØ(½ÝÖ" à
2. ¦Øa.§$Ž(Jkêi ê=Škêi êêƒÓ
3. kž‡äN©ÛØþ?§·õ3˜ §ØUÏOŽ‰(JE¤LŒØ
2.4 Šã{††‚[Ü
^Šã{?nêâ‡5¿‹IŠŒ†‹I¶'~À‡Ü·§ÿþêâ:‡^AÏÎÒI
P§k
žÿ„I‡^éê‹I’Šã.
éu‚5'X§Œ±¦^¦{‰†‚[Ü
y = a0 + a1x
Ù¥
a1 =
x̄y − x̄ȳ
x̄2 − (x̄)2
a0 = ȳ − a1x̄
ك'5dƒ'Xê
r =
x̄y − x̄ȳ√
[x̄2 − (x̄)2][ȳ2 − (ȳ)2]
‰Ñ.
3
3 ¢SN
1. ^iIkºÿþgNÈ¿OŽ(JØ(½Ý
2. ^Ú^ÿ‡ìÿþg¥NÈ¿OŽ(JØ(½Ý
4 êâL‚
4.1 ^iIkºÿþgNÈ
‘8 D/cm d/cm H/cm h/cm
":Öê 0.000 0.000 0.000 0.000
1 2.810 1.996 4.520 3.200
2 2.812 1.992 4.522 3.206
3 2.810 1.994 4.520 3.208
4 2.808 1.994 4.520 3.200
5 2.810 1.996 4.522 3.198
6 2.810 1.992 4.520 3.204
²þŠ 2.810 1.994 4.521 3.203
²þŠIO 5× 10−4 7× 10−4 4× 10−4 2× 10−3
Ĥì#IO 2× 10−3 2× 10−3 2× 10−3 3× 10−33
?":²þŠ 2.810 1.994 4.521 3.203
4.2 ^Ú^ÿ‡ìÿþg¥NÈ
ÿþgê ":Öê 1 2 3 4 5 6
d/mm -0.001 12.697 12.696 12.695 12.695 12.696 12.695
²þŠ ²þŠIO Ĥì#IO ?":²þŠ
12.696 4× 10−4 4× 10−3 12.697
5 êâ?n9(J
5.1 ^iIkºÿþgNÈ
ÿþ(J:
D̄ ± σD = (2.810± 0.002)cm
d̄± σd = (1.994± 0.002)cm
H̄ ± σH = (4.521± 0.002)cm
h̄± σh = (3.203± 0.003)cm
OŽ(J:
V =
π
4
(D̄2H̄ − d̄2h̄) = 18.04cm3
4
σV =
π
4
√
(2D̄H̄σD)2 + (D̄2σH)2 + (2d̄h̄σd)2 + (d̄2σh)2 = 0.05cm3
V ± σV = (18.04± 0.05)cm3
5.2 ^Ú^ÿ‡ìÿþg¥NÈ
ÿþ(J:
d̄± σd = (1.2697± 0.0004)cm
OŽ(J:
V =
1
6
πd̄3 = 1.0718cm3
σV =
1
2
πd̄2σd = 0.001cm3
V ± σV = (1.072± 0.001)cm3
6 ?Ø
ÿþgݞuyduiIkº"à¡ÈL§éJykº"੪†.²1bܧ…
Ø´Öê. ¢¥<æ^‰{yòiIl"£Ä˜ã§,†Ã±iI§¦kºÿ
Ý"à†.>§dž†Ã½d ˜§,mÕeíÄ̺§¦Ìº.܆÷;
—bܧḏ†iIØA2kƒé£Ä§,Ø;Új§Öê.
7 Š’
1. (1)1  (2)4  (3)2  (4)6 
2. (1)
c =
ab
b− a
=
9.9× 999.9
999.9− 9.9
=
9.9× 103
990.0
= 10(cm)
(2)
y = e−x
2
= e−9.242 = e−85.4 = 8.15× 10−38
(3)
y = lnx = ln 56.7 = 4.04
(4)
y = cosx = cos 9.4◦ = 0.99
3. (a)
σV =
π
4
√
(2RHσR)2 + (R2σH)2 + (2rhσr)2 + (r2σh)2
(b)
σρ = ρ0
√
(− m2
(m1 −m2)2
σm1)2 + (
m1
(m1 −m2)2
σm2)2
5
4. Y(1)
L = L1 +
1
2
(d1 + d2)
dž
σL =
√
σ2
L1
+ (
1
2
σd1)2 + (
1
2
σd2)2 = 0.9µm
Y(2)
L = L2 − (d1 + d2)
dž
σL =
√
σ2
L2
+ σ2
d1
+ σ2
d2
= 1.3µm
w,ÀJY(1)
5. ¦^iIkºÿþd2§ÙØ(½ÝOσd2 = 0.002cm.ù§Œ±¡È
S = L1L2 −
π
4
(d2
1 + d2
2) = 62.8cm2
9ÙØ(½Ý
σS/S =
√
(L2σL1)2 + (L1σL2)2 + (
π
2
d1σd1)2 + (
π
2
d2σd2)2/S = 0.2%
ù«{Œ1.
7. (1)d
g =
2h
t2
Œ
δg
g
=
√
(
δh
h
)2 + (−2
δt
t
)2
Ù¥
δh
h
= (30− 20)× 1× 10−5 = 1× 10−4,
δt
t
= −1× 10−4

δg
g
= 1.4× 10−4
…dgLˆªŒAT´ Œ§g = 980.0× (1 + 1.4× 10−4)cm/s2 = 980.1cm/s2
(2)16, 5
10. dK¿
σy =
√
0.00052 + 0.012 = 0.01(mm)
σf = 0.05kHz
λ =
īy − īȳ
ī2 − (̄i)2
= 8.75mm
ƒ'Xê
r =
īy − īȳ√
[ī2 − (̄i)2][ȳ2 − (ȳ)2]
= 0.999969
6

σλ = λ
√
1/r2 − 1
n− 2
= 0.02mm,n = 10

c = fλ = 346.3m/s
σc =
√
(λσf )2 + (fσλ)2 = 0.9m/s
11. (1)ㄋI’
(2)k2 = 0.079 §å−0.206§r2 = 0.99933
(3)k1 = 12.64 §å2.64§r1 = 0.99933
ƒÓ§Ï½Âƒ'Xꞧƒ'5ØA6u‹I¶À§Ù'X
r =
√
k1k2
7