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2 Excel ではじめる数値解析 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.
3 Excel URL
4 i Microsoft Windows Excel VBA Excel 2013 Excel Excel
5 ii VBA Excel 69 70
6 iii Excel
7
8 1 spreadsheet Microsoft Excel Excel Excel = 1 2 A B C 2 C2 Enter 1.1
9 A1 B1 =A1+B1 1 =a1+b1 A1 B1 1.1 ( ) = = =2*3 4 2 =4/2 2 3 =2^3 3 {1+2 (2 + 3)} =3*(1+2*(2+3)) SUM( ) AVERAGE( ) A1 A10 10 =SUM(A1:A10) : 1.2 E1 B1C1 E1 E2 F3 E1 1 A1 example number
10 Ctrl C Ctrl+C E2 Ctrl+V =B2+C2F3 =C3+D3 1.4 E1 B1B1 E1 E2 E2 B2 F3 F3 B3 Excel $ B1D3 1 9 A1 1.1 G1I3 B1D3 A1
11 4 1 G1 =B1/$A$1 A1 G1 H1 I1 I1 1.5 G2I3 G1I1 I3 G1I3 Ctrl D Ctrl+DCtrl+DD Down Ctrl+RR Right G1I3 = /$A$1A1 1.6 $A$1 A$1 $A1 F4 $A$1 F4 A1 $A$1 A$1 $A1 A1 1.2 J1L3 B1D3 B J1 =B1/$B1 K1L1 J1L1 J3L3 J2 =B2/$B2
12 1.1 5 J3 =B3/$B3 B K1 =C1/$B1L3 =D3/$B3 B B4D6 B1D3 1 B4 =B1/B$1 B5B6 C4D6 B5 =B2/B$1D6 =D3/D$ # =2/0 #DIV/0!0 1.2 #### # A1 B1 B1 A1 A1 =A1
13 #DIV/0! 0 0 #NAME? A1 A #VALUE! =A1+B1 A1 #N/A Not Available #### 1.2 VBA Excel Visual Basic for ApplicationsVBA VBA VBA BASIC Excel Word Microsoft 1.9
14 x x, x 2,x 3, f(x) x = a = f (n) n f(x)=f(a)+ 1 1! f (a)(x a)+ 1 2! f (a)(x a) ! f (a)(x a) n! f (n) (a)(x a) n + = f(a)+ i=1 1 i! f (i) (a)(x a) i (3.1) x = a x = a Brook Taylor f(x) =x 20, a =1 2 f(1) = 1 20 =1, f (x) =20x 19
15 30 3 f (1) = =20, x a = = f(1.0002) f(1) + f (1) = = (3.1) (3.1) 2 x 1 3 x 2 n +1 x n (3.1) f(x) =b 0 + b 1 (x a)+b 2 (x a) 2 + b 3 (x a) 3 + (3.2) Δx = x a x = a (3.2) f(a) =b 0 2 (x a) a a =0 b 0 = f(a) (3.2) x f (x) =b 1 +2b 2 (x a)+3b 3 (x a) 2 + (3.3) x = a (3.3) f (a) =b 1 2 b 1 = f (a) (3.3) 1 f (x) =2b b 3 (x a)+4 3b 4 (x a) 2 + (3.4) x = a (3.4) f (a) =2b 2 2 b 2 = f (a) 2 b 3 = f (a) 3 2, b 4 = f (4) (a) 4 3 2,, b n = f (n) (a) n! 2 f(x) f(a)+ 1 1! f (a)(x a) (3.5) 3.1 (a, f(a)) f(x) f(x) A x a
16 f(x) 3.2 (a, f(a)) x a f (x) f (x) 3.1 f (a) (x, f(x)) f (x), f (a) 3.2 (x, f(x)) f (x) 3.1 f(x), f(a) f (x), f (a) f (x) =f (a)+f (a)(x a) (3.6) f(x) f(x) f(a)+ f (a)+f (x) (x a) 2 = f(a)+ f (a)+{f (a)+f (a)(x a)} (x a) 2 = f(a)+ f (a) 1! (x a)+ f (a) (x a) 2 (3.7) 2! 3 f (x) x = a Excel
17 f(x) =e x x =0 f(x) =e x e x (3.1) f(x) =e a + 1 1! ea (x a)+ 1 2! ea (x a) ! ea (x a) 3 + (3.8) x =0 (3.8) a =0e 0 =1 f(x) =1+x + 1 2! x ! x3 + (3.9) x =0Colin Maclaurin (3.9) x =0 Excel Excel 1 A x B f(x) =e x CE A2, A3-1, -0.9 A2, A3 A3 A22 A B e x Excel EXP( ) C x 1 1+x D x 2 1+x + x 2 /2! C x 2 /2! E x 3 1+x + x 2 /2! + x 3 /3! D x 3 /3! Excel FACT( ) B2E2 3.4
18 B2E22 B2 Shift E22 Ctrl+D x =0 1 B AE AE 3.6 e x x =01 f(x) =1+x x 1 e x x = ±0.5 3 x = 0.51 e x x =0.5=ABS(C17-B17)/B17 1 =ABS(D17-B17)/B17 2 =ABS(E17-B17)/B17 3 ABS( )
19 OK1 9.0%2 1.4%3 0.2% 3 e (0.5)2 2 + (0.5)3 6 (3.10) x =0.11 e = f(x) =sinx x =0 (3.1) f(x) =sinx, a =0 f(x) =sinx, f (x) =cosx, f (x) = sin x, f (x) = cos x, f (4) (x) =sinx, x =0sin 0 = 0, cos 0 = 1 x 2 x 4 x sin 0 = 0 (3.1) f(x) x 1 6 x x5 Excel B ππ x A π B A B2 A π π PI( ) C2 B sin 3.7
20 D2 x 1 E2 x 3 F2 x 5 x Excel 2 B2 B2F2 B22F22 BF 3.85 π/2π/ x 1 3.9
21 92 7 simulation sleonhard Euler A 0, m B Excel x y g t [s] m (x, y) m d2 x =0 dt2 (7.1) m d2 y dt = mg 2 (7.2) m d 2 x =0 dt2 (7.3) d 2 y dt = g 2 (7.4) x, y Δt =0.1s Δt [s]
22 Δt [s] ẋ dx/dt, ẍ d 2 x/dt 2 x(t + Δt) = x(t) +ẋ(t) Δt (7.5) y(t + Δt) = y(t) +ẏ(t) Δt (7.6) ẋ(t + Δt) = ẋ(t) +ẍ(t) Δt (7.7) ẏ(t + Δt) = ẏ(t) +ÿ(t) Δt (7.8) 40 km 2 80 km Δt [s] =+ = Δt Δt [s] =+ = Δt Δt [s] (7.5)(7.8) (7.3), (7.4) ẍ(t) =ẍ(t + Δt) = 0 (7.9) ÿ(t) = ÿ(t + Δt) = g (7.10) t + Δt (7.7)(7.9) 1 (7.10) (7.8) ẏ(t + Δt) =ẏ(t) g Δt (7.11) A 0, v θ
23 x(0) = 0, y(0) = 0, ẋ(0) = v cos θ, ẏ(0) = v sin θ (7.12) AB L = 100 m B h =10m 7.2 D2E D5 Enter X D6D7 Enter Y E6E7 Enter D8 Enter X D9 Enter Y E9 Enter OK
24 OK 7.7 game VBA VBA 1y<=0 B x>l s 2 B <=h2 >=h1 1 ForNext Do WhileLoop
25 B Boolean Boolean TrueFalse 2 Dim A BAnd If ( A And B) Then yl yl h1 yl h2 >=<= yl xbybxy B x>=l B B
26 7.1 Dim hit As Boolean Dim arrival As Boolean hit = False: arrival = False v = [B1] theta = 3.14 * [B2] / 180 L = [B3] h1 = [B4] h2 = [B5] g = 9.8 vx = v * Cos(theta) vy = v * Sin(theta) x = 0 : y = 0 xb = 0 : yb = 0 Calculate dt = 0.01 Do While (y >= 0) x = x + vx * dt y = y + vy * dt vy = vy - g * dt [D9] = x [E9] = y Calculate If (arrival = False And x >= L) Then arrival = True yl = yb + (y - yb) * (L - xb) / (x - xb) If ( yl <= h2 And yl >= h1 ) Then hit = True Exit Do End If End If If ((x > L + 10) Or (x < 0)) Then Exit Do End If xb = x: yb = y Loop If hit Then MsgBox("") Else MsgBox("") End If B False v B1 theta B2 π 180 L B h1 h2 g 9.8 m/s 2 (7.12) x (7.12) y (7.12) (x, y) dt Δt [s] y>=0 (7.5) x (7.6) y (7.11) vy D9E9 B B yl hit True Do B L+10 Do hit True
27 98 7 (7.5)(7.6) t + Δt [s] t [s] = 1 x=0 : y=0 1 Excel game B1 B2 (7.5)(7.10) 2 B1 B2 Enter m [kg] k [N/m] t x [m]1 = ẋ = dx/dt [m/s]1 = ẍ = d 2 x/dt 2 [m/s 2 ] kx 2 mẍ = kx (7.13) mẍ + kx = 0 (7.13) x = A cos ωt + B sin ωt (7.14) ω = k/ma, B (7.14)
28 COE Excel C FAX Printed in JapanISBN
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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1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 0 < t < τ I II 0 No.2 2 C x y x y > 0 x 0 x > b a dx
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
最新耐震構造解析 ( 第 3 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 3 版 1 刷発行時のものです.
最新耐震構造解析 ( 第 3 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/052093 このサンプルページの内容は, 第 3 版 1 刷発行時のものです. i 3 10 3 2000 2007 26 8 2 SI SI 20 1996 2000 SI 15 3 ii 1 56 6
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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
1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π
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1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1
ABCD ABD AC BD E E BD : () AB = AD =, AB AD = () AE = AB + () A F AD AE = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD AB + AD AB + 7 9 AD AB + AD AB + 9 7 4 9 AD () AB sin π = AB = ABD AD
1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0
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