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1 ( )
2 i
3 CV F CV F CV F CV F CV F CV F CV F CV F ii
4 iii
5 ( 2 ) CV F CV F CV F ( ) CV F ( ) CV F CV F CV F ( 1 ) iv
6 p = p = p = p = p = p = p = p = p = p = ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 3.11 ) ( 3.12 ) l =2.1R l =2.5R l =3.0R l =3.5R v
7 4.17 l =3.9R vi
8 ( 1 ) vii
9 [ (1982)]
10 1.1: :
11
12 ( 2 ) χ θ([ (1998)]) CV F([ (1998)]) ( 3 ) 104 CV F CV F CV F CV F ( 4 ) 1.3: 4
13 [, (1956)] 1 3 ([, (1956)]) ( ) ( ) 2 5
14 2.1.2 [ (1998)] 4 6
15 2.2 1) 2) 3) [ (1974)] p R(p) R(p) =0 (p<p c ) R(p) > 0 (p>p c ) p c R(p) p c 0 <p c < 1 2 7
16 [ (1974)] R(p) 3 R(p) p c [ (1973)] 2 1 ( ) % 4 55% 1/5 2/5 2 1/ [ (1982)] % 8
17 % 1% % 1% 70% ([ (1998)] [, (1999)] [,, (1999)] [,, (2000)]) [ (1998)] p c p c 1 ( ) 1 ( ) ρ d p CV F(Covering Volume Fraction) CV F CV F ρ d /2 CV F =1 exp (πρp c (d /2) 2 ) (2.1) CV F 9
18 2.2.5 [ (1999)] (2.2.3 ) d ( ) 1 S e S S w n w d = Se S w /S S w nw (2.2) D D =9.5x +8.0y +5.2z +4.0p (2.3) x y z p (1) d/d < 1.0 (2) 55% (2.2.4 ) 55% 10
19 20% 16% 9.5% 55% (3) d<5.2 D =5.2 d/d < [ (1993)] 4 250m 1) 2) 250m 250m 9 3) 60 [ (1985)] m ) 2) 2 11
20 2 V = δ r(w) g(h) (1 c ) δ = a a Vw+b Vm a +b +d V d a+d r(w) = w (2.4) g(h) = h a d a b c w h V d V w V m (m) (m) (m/sec) (%) ( 0.45m/min 0.33m/min 0.38m/min) (0.87m/min) (0.71m/min) δ [ (1999)] 2 α S s 1 s 2 s 3 s 4 k 1 =0.36 k 2 =0.64 k 3 =
21 k 4 =1.00 α = 4i=1 k i s i S β β 0 n S S 0 β 0 = S0 S n 1 a b c d p i l 1 =2.25 l 2 =2.16 l 3 =2.08 l 4 = β = β 0 l i p i (2.5) i=1 p 1 = a n, p 2 = b n, p 3 = c n, p 4 = d n (2.6) 1 y α β y = a 0 + a 1 α + a 2 e bβ a 0 = a 1 = a 2 = b = α : t =4.05 β : t =13.73 R 2 =
22 : 2.1: [ (1974)] [ (1974)] [ (1974)] [ (1973)] [ (1998)] 1 2 [ (1999)]
23
24 ([ (1998)]) [, (1956)] θ t 200 C θ(t) =6200(e 10t e 15t )+200 (2.7) 1 θ 1 (t) =θ(t) C 1 θ 1 (t) = θ(t) 1110 C 2 θ 2 (t) = 3 4 θ 1(t) 833 C 3 θ 3 (t) = 1 2 θ 1(t) 550 C 4 θ 4 (t) = θ 1(t) 260 C d h h = pd 2 (p ) ( ) p 10m 1 2 d =0 (2.8) 2 3 h =0.82d 2 (2.9) 3 4 h =0.15d 2 (2.10) 4 h =0.04d 2 (2.11) 16
25 θ(t) θ 1 (t) θ 2 (t) θ 3 (t) θ 4 (t) t 2.2: [, (1956)] h d =0 h =0.82d 2 h =0.15d 2 h =0.04d 2 d 2.3: [, (1956)] 17
26 2.3.2 a d t V =(a + d)/t ( ) ([ (1997)]) 2.2: t(min) V (m/min) D(m) t 0 = a + 8d D i (1 ) 1+0.1ν t i = a + 8d D i α( ν ν 2 ) α =1.6 t t V = n α(a + d)( ν ν2 ) a + 8d D i n = (a + b ) (1 c ) a + b 0.6 t = a + 8d D ν 2 V = n (a + d)( ν2 ) a + 8d D t = a + 8d D ν 2 V = n (a + d)( ν2 ) a + 8d D a (m) d (m) ν (m/sec) a b c D 0 =1.15( ν) D i = β i D 0 β i D =1.15( ν) D =1.15( ν) [ (1997)] ν 18
27 2.3.3 [ (1972)] =D/2( D ) τ τ 0 = a + 8d δ (1 ) 1+0.1ν τ 1 = a + 8d δ α( ν ν 2 ) α = 1.6 τ +14 τ +25 T t( 2.2) τ x K ( ) a K = 2 + d +(x T 0 ) 1 (a + d) T 1 ( ) a x x T 0 K = 2 + d T ( ) 0 a K = 2 + d +(x T ) 1 (a + d) T ( ) a x x T K = 2 + d T ( ) a K = 2 + d +(x T ) 1 (a + d) T ( ) a x x T K = 2 + d T 19
28 2.3.4 [ (1982)] PC t 0 = x + x 8 a + 8d D i 1+0.1ν (2.12) d =0 a =8 ν =1.5 t 0 =17.5 x =10 D m D k h 4 h =0.04D m 2 h =0.82D k 2 ((2.11) ) ((2.9) ) D k = D m /4 t k0 D 1k t k0 = a + 10d D 1k 1+0.1ν D 1k = D m 4 (2.13) (2.14) m 3 20
29 [, (1983)] m n 2 1 ( ) r 1 r 2 Z E(Z) V (Z) r (2) 1 r 2 r (4) 1 r 2 E(Z) = A 1 b (3) A 2 b (5) r (3) 1 r (2) 2 r 1 V (Z) = 2B 1 b (5) +2B 2 (4) r 2 (2) b (6) 2F 1 r 1 (5) r 2 (2) b (7) +2(D 2 F 2 ) r 1 r (7) 1 r (2) 2 r 1 +2D 1 b (9) +2D 3 (6) r 2 (2) b (8) (8) r (2) 2 b (10) +E(X) E(Y ) {E(X)+E(Y )} 2 X = ( )+( ) Y = ( ) A 1 = 2(b a) A 2 = b 2a +4 B 1 = 6b 12a +16 B 2 = A 1 2 D 1 = 2b 6a +16 (A 2 + B 1 +6b 11a + 16) 21
30 D 2 = 2b 6a +18 D 3 = A 2 2 F 1 = 12b 32a +80 (D 1 + D 2 +2b 5a + 12) F 2 = A 1 A 2 (F 1 +10b 22a + 48) r i (k) = r i (r i 1) (r i k +1) b (k) = b(b 1) (b k +1) a = m + n b = mn [ (1988)] [, (1989)] [, (1989)] ζ r C ρ ˆζ = C +4r Cρ + ρπr 2 (2.15) 22
31 r 0 C + η (r r 0 ) ˆζ = (2.16) 1 (1 C η 0 )exp( (η η 0 )) (r >r 0 ) η =4r Cρ + ρπr 2 η 0 =4r 0 Cρ + ρπr0 2 1 s C = sρ s = α ρ (2.17) [ (1998)] CV F [, (1989)] [ (1998)] [ (1998)] p c [ (1974)] R χ 1 N k i 23
32 n i i i n i χ = ki=1 n i 2 N (2.18) θ 1 θ = 1 N max {n i i =1,..., k} χ VA χ i 1 s i (2.18) n i s i χ A χ A = ki=1 n i s i N S 0 χ VA = ki=1 n i s i S 0 N (2.19) [ (1998)] CV F CV F (1) 3 (2) (1) (2.1) CV F 3 (2) (2.1) ([, (1989)] (2.16) 24
33 (2.1) p c =1 CV F =1 exp (πρ(d /2) 2 ) (2.20) (2.16) C =0 r r 0 =0 ˆζ =1 exp ( (ρπr 2 )) (2.21) [ (1986)] (2.16) [ (1986)] (2.16) r
34 3 3.1 [ (1998)] CV F CV F CV F CV F CV F CV F 3.2 CV F CV F 6 ( ) ( ) 6 40m 26
35 40m 3000m 2 2% 104 (3.1) CV F [ (2001)] [ (2001)] 2 ( 6m) (1) (a) (b) (c) (2) CV F 2.3 ( ) :( ) :( ) =4:2:1 10m 4 (2.11) h =0.04d 2 2 6m h =6 d =5 6=12.25(m) d 10m 2 10m D 10 D10 w = 12(m) D10 b = 6(m) D10 k = 3(m) 27
36 3.1:
37 6m a D a D 10 a ( 10m D 10 ) =( a D a ) a D a Da w = 12 ( a ) = 4.34 a Da b = 6 ( a ) = 2.86 a Da k = 3 ( a ) = 1.98 a D t a = 0 (3.1) a A a = A CV F CV F ([, (1989)] ) CV F
38 1 3.2: ( 2 ) 30
39 (2.19) χ VA χ VA = ki=1 n i s i S 0 N 3.3 CV F CV F 3.3 CV F 0.05 CV F CV F 3.3: CV F CV F 3.1 CV F ([, (1989)]) ([ (1988)]) CV F [ (1999)] (2.2.7 (2.6) ) 31
40 CV F [ (1999)] β 3.4 β CV F β β CV F CV F β 3.4: CV F CV F 3.5 CV F χ VA CV F 0.6 χ VA 0.1 CV F 0.6 χ VA 3.6 CV F χ VA CV F 0.6 χ VA CV F 0.6 χ VA CV F CV F CV F 32
41 χ VA CV F 3.5: CV F ( ) χ VA CV F 3.6: CV F ( ) 33
42 3.4 CV F CV F CV F L 3.7 (a) (b) 3.7: (a) (b) 3.8 L/S 0 χ VA L/S 0 34
43 χ VA L/S 0 3.8: L/S CV F 3.9: CV F 35
44 CV F L/S 0 CV F L/S L/S 0 CV F χ VA CV F CV F L/S 0 χ VA 3.10 CV F L/S 0 χ VA L/S 0 CV F 3.10: CV F χ VA CV F CV F L/S 0 CV F ( ) L/S 0 L/S 0 χ VA CV F L/S 0 CV F L/S 0 ([ (1986)]) 36
45 3.4.2 CV F [ (1999)] β CV F CV F β (2.2.7 ) CV F [ (1998)] 4 (2.2.4 ) 3 χ VA CV F χ VA CV F χ VA : S 0 L/S 0 β CVF (m 2 ) ( /ha) (m/ha) (m) χ VA
46 3.11: 2 38
47 3.12: 5 39
48 3.13: 1 40
49 3.14: 2 41
50 0.1 ( 2 5 ) 0.2 ( 1 2 ) 2 1) 2)
51 3.5 CV F CV F CV F CV F ) 2) 3.15 ([ (1999)]) (1)
52 3.15: 44
53 3.5.3 ( ) 1 6m ( 3.16) CV F χ VA : ( 1 ) CV F χ VA a b /2 2 2 (3.4.2 ) CV F
54 3.16: 46
55 ( ) : 47
56 : 48
57 χ VA CV F 3.18: CV F ( 1 ) 0.02 CV F a. b CV F χ VA χ VA
58 3.19:
59 3.20: 51
60 a b 3.21: 1 52
61 3.5.6 [ (1998)] p c CV F CV F 3.5 CV F CV F CV F CV F CV F 3.5 1) 2) 5 5 3) 2 4) p χ N θ (2.5.1 ) p 13 1 p 21 53
62 p : p = : p =14 54
63 3.24: p = : p = : p = : p =17 55
64 3.28: p = : p = : p = : p =19 56
65 p χ θ χ θ p =20 p : 3.33: 57
66 p =13 p =15 p =15 60% ([ (1998)]) CV F (3.3 ) CV F p =3 p =19 p =5 p =9 p =17 p =13 p = : 58
67 3.7 CV F CV F CV F CV F 59
68 4 4.1 ( ) ((3.1) ) ( 3 ) 2 2 ( 4.2) 60
69 4.1: ( 1 ) 61
70 4.2: ) 1 2) 1 3)
71 2 2 63
72 4.3: 1 ( 1 ) 64
73 4.4: 1 ( 1 ) 65
74 4.5: 1 ( 1 ) 66
75 ) 2) 1) 2) (1) (2) 1 (3.5.1 ) 67
76 ) 2) 3) 4) 5) 6) 68
77 C 1 m (m +1) C 1 C 1 n x 1,..., x n ( 0 <x 1 < <x n ) x 1,..., x n g 1,..., g n 2 g i 1 g i A i A i = xi x i 1 C 1 dx A 1 = = A m+1 x 1,..., x m C 1 (m+1) ( 4.6) 4.4 x 1 x 2 x 3 O 4.6: 69
78 1 2 C 2 m 2m C 2 (m 1) m 1 2 C 2 2m ( 4.7) 4.7: 70
79 m 2m (i + j) (i +1)(j +1) 3 (i + j) (i +1)(j +1) ABC A BC i X 1,..., X i i BC j 1 j ABC (i +1)(j +1) ( 4.8) A B X 1 X 2 X 3 C 4.8: BC j 1 1 (i + j) (i +1)(j +1) 71
80 4 (i + j) (i +1)(j +1) ABCD AB i (i +1) ABCD AD j (j +1) ABCD (i +1)(j +1) ( 4.9) A D B C 4.9: ( 4.10) 5 ( 4.11) 72
81 4.10: 2 ( 3.11 ) 73
82 4.11: 5 ( 3.12 ) 74
83 l 2 g 1 g 2 g 1 l 1 ( 0 <l 1 <l/2) g 1 Y 1 Y 1 g 2 Y 2 Y 2 g 1 g 2 M 1 M 2 ( 4.12) g 1 Y 1 g 2 X Y 2 M 2 Y 2 O M 1 Y : 2 g 1 2 S 1 A 1 A 1 = R 2 sin 1 l 1 2R 1 2 l 1 R 2 l g 2 2 S 2 A 2 A 2 = R 2 sin 1 l l 1 2R 1 2 (l l 1) R 2 (l l 1) 2 4 S 1 S 2 A 12 2 χ 2 χ 2 = A (A 1 A 12 ) 2 +(A 2 A 12 ) 2 +(πr 2 A 1 A 2 + A 12 ) 2 = 4A (πR 2 2A 1 2A 2 )A 12 +2A A A 1 A 2 2πR 2 (A 1 + A 2 )+π 2 R 4 75
84 S 1 S 2 A 12 g 1 OM 1 g 2 OM 2 θ 12 (0 <θ 12 <π) i) 0 <θ 12 < sin 1 l l 1 2R sin 1 l 1 2R A 1 A 2 A 12 = A 1 ii) sin 1 l l 1 2R sin 1 l 1 2R <θ 12 < sin 1 l l 1 2R +sin 1 l 1 2R g 1 g 2 A 12 2 g 1 g 2 X A 12 =( OY 2 Y 1 ) ( OXY 1 ) ( OXY 2 ) ( OY 2 Y 1 ) = 1 ( 2 R2 sin 1 l 1 l l ) 2R +sin 1 1 2R θ 12 ( OXY 1 ) = 1 ( ) l1 2 2 v 1 p 1 ( OXY 2 ) = 1 ( v 2 + l l ) 1 p p 1 = R 2 l p 2 = R 2 (l l 1) 2 4 v 1 = p 2 sin θ 12 + v 2 cos θ 12 v 2 = p 2 cos θ 12 p 1 sin θ 12 A 12 = p 1p 2 p p sin θ 12 2tanθ 12 2 R2 θ 12 + C C = 1 ( 2 R2 sin 1 l 1 l l ) 2R +sin R 4 {(p 1 p 2 )l 1 + lp 2 } iii) sin 1 l l 1 2R +sin 1 l 1 2R <θ 12 <π A 1 A 2 A 12 =0 l 2.1R 2.5R 3.0R 3.5R 3.9R l 1 θ l 1 = l 2R θ 12 = π/2 1) 2R g 2 76
85 2) g 2 1 g θ 12 l χ/(πr 2 ) l 1 θ : l =2.1R χ/(πr 2 ) l 1 θ : l =2.5R 77
86 χ/(πr 2 ) l 1 θ : l =3.0R χ/(πr 2 ) l 1 θ : l =3.5R 78
87 χ/(πr 2 ) l 1 θ : l =3.9R
88
89 5 5.1 CV F CV F CV F CV F 81
90 5.2 [ (1998)] ([ (1982)]) 70% CV F (1) (1a) CV F (1b) (1c) (1d) (1a) CV F CV F 82
91 CV F (1b) (1c) (1d) (1a) (2) 1 (2a) (2b) (2c) (2d) (2a) (2b) (2c) ( ) (2d) 83
92 [ (1998)] :,, [,, (1999)],,,, : ( 2)- -, 525, , [,, (2000)],,, : ( 3)- -, 534, , [, (1999)], : - -, 516, , [ (1982)] :, [ (2001)] :, [ (1986)] :, OR , [ (1988)] :, 23, 19 24, [, (1989)], :, 24, , [, (1983)], :, 18, 37 42,
93 [ (1999)] :, [ (1999)] :,, [ (1973)] : - -, 91, 18 19, [ (1985)] :, [ (1993)] : ( 3 ), [ (1997)] :,, 3, [ (1999)] : - -,, [, (1956)], :, 21., [ (1974)] :, 132, 45 52, [ (1972)] :,, [ (1982)] :, 22, ,
t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ
4 5 ( 5 3 9 4 0 5 ( 4 6 7 7 ( 0 8 3 9 ( 8 t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ S θ > 0 θ < 0 ( P S(, 0 θ > 0 ( 60 θ
70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +
( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n
1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
zz + 3i(z z) + 5 = 0 + i z + i = z 2i z z z y zz + 3i (z z) + 5 = 0 (z 3i) (z + 3i) = 9 5 = 4 z 3i = 2 (3i) zz i (z z) + 1 = a 2 {
04 zz + iz z) + 5 = 0 + i z + i = z i z z z 970 0 y zz + i z z) + 5 = 0 z i) z + i) = 9 5 = 4 z i = i) zz i z z) + = a {zz + i z z) + 4} a ) zz + a + ) z z) + 4a = 0 4a a = 5 a = x i) i) : c Darumafactory
, 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p, p 3,..., p n p, p,..., p n N, 3,,,,
6,,3,4,, 3 4 8 6 6................................. 6.................................. , 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p,
Part () () Γ Part ,
Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35
I II III IV V
I II III IV V N/m 2 640 980 50 200 290 440 2m 50 4m 100 100 150 200 290 390 590 150 340 4m 6m 8m 100 170 250 µ = E FRVβ β N/mm 2 N/mm 2 1.1 F c t.1 3 1 1.1 1.1 2 2 2 2 F F b F s F c F t F b F s 3 3 3
(iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y = 0., y x, y = x. (v) 1x = x. (vii) (α + β)x = αx + βx. (viii) (αβ)x = α(βx)., V, C.,,., (1)
1. 1.1...,. 1.1.1 V, V x, y, x y x + y x + y V,, V x α, αx αx V,, (i) (viii) : x, y, z V, α, β C, (i) x + y = y + x. (ii) (x + y) + z = x + (y + z). 1 (iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y
Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e
7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z
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1 17 () BAC9ABC6ACB3 1 tan 6 = 3, cos 6 = AB=1 BC=2, AC= 3 2 A BC D 2 BDBD=BA 1 2 ABD BADBDA ABC6 BAD = (18 6 ) / 2 = 6 θ = 18 BAD = 12 () AD AD=BADCAD9 ABD ACD A 1 1 1 1 dsinαsinα = d 3 sin β 3 sin β
i ii iii iv v vi vii ( ー ー ) ( ) ( ) ( ) ( ) ー ( ) ( ) ー ー ( ) ( ) ( ) ( ) ( ) 13 202 24122783 3622316 (1) (2) (3) (4) 2483 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 11 11 2483 13
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E
17 ( ) II III A B C(100 ) 1, 2, 6, 7 II A B (100 ) 2, 5, 6 II A B (80 ) 8 10 I II III A B C(80 ) 1 a 1 = 1 2 a n+1 = a n + 2n + 1 (n = 1,
17 ( ) 17 5 1 4 II III A B C(1 ) 1,, 6, 7 II A B (1 ), 5, 6 II A B (8 ) 8 1 I II III A B C(8 ) 1 a 1 1 a n+1 a n + n + 1 (n 1,,, ) {a n+1 n } (1) a 4 () a n OA OB AOB 6 OAB AB : 1 P OB Q OP AQ R (1) PQ
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,
[ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b
18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C
8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
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