untitled

Similar documents
untitled

ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 (

(1) 1.1

untitled

DVIOUT-HYOU

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

A

ad bc A A A = ad bc ( d ) b c a n A n A n A A det A A ( ) a b A = c d det A = ad bc σ {,,,, n} {,,, } {,,, } {,,, } ( ) σ = σ() = σ() = n sign σ sign(

29

1.500 m X Y m m m m m m m m m m m m N/ N/ ( ) qa N/ N/ 2 2

０４年度LS民法Ⅰ教材改訂版.PDF

untitled


DVIOUT

6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

3.300 m m m m m m 0 m m m 0 m 0 m m m he m T m 1.50 m N/ N

9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x

() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n (

2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l

untitled

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI

(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 lim f(x, y) (x,y) (a,b) ( ) ( ) lim limf(x, y) lim lim f(x, y) x a y b y b x a ( ) ( ) xy x lim lim lim lim x y x y x + y y x x + y x x lim x x 1

I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )

all.dvi

R R 16 ( 3 )

solutionJIS.dvi

Part y mx + n mt + n m 1 mt n + n t m 2 t + mn 0 t m 0 n 18 y n n a 7 3 ; x α α 1 7α +t t 3 4α + 3t t x α x α y mx + n

II (10 4 ) 1. p (x, y) (a, b) ε(x, y; a, b) 0 f (x, y) f (a, b) A, B (6.5) y = b f (x, b) f (a, b) x a = A + ε(x, b; a, b) x a 2 x a 0 A = f x (

.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 =,

プリント

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6

e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,,

v er.1/ c /(21)

1 1.1 ( ). z = a + bi, a, b R 0 a, b 0 a 2 + b 2 0 z = a + bi = ( ) a 2 + b 2 a a 2 + b + b 2 a 2 + b i 2 r = a 2 + b 2 θ cos θ = a a 2 + b 2, sin θ =

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f


.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g(

7. y fx, z gy z gfx dz dx dz dy dy dx. g f a g bf a b fa 7., chain ule Ω, D R n, R m a Ω, f : Ω R m, g : D R l, fω D, b fa, f a g b g f a g f a g bf a

untitled

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P

1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =

( )

LLG-R8.Nisus.pdf

untitled

IMO 1 n, 21n n (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a


x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)

熊本県数学問題正解

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google

untitled

w

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.

he T N/ N/

変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,


II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R

Akito Tsuboi June 22, T ϕ T M M ϕ M M ϕ T ϕ 2 Definition 1 X, Y, Z,... 1

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 :

x y x-y σ x + τ xy + X σ y B = + τ xy + Y B = S x = σ x l + τ xy m S y = σ y m + τ xy l σ x σ y τ xy X B Y B S x S y l m δu δv [ ( σx δu + τ )

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

さくらの個別指導 ( さくら教育研究所 ) 1 φ = φ 1 : φ [ ] a [ ] 1 a : b a b b(a + b) b a 2 a 2 = b(a + b). b 2 ( a b ) 2 = a b a/b X 2 X 1 = 0 a/b > 0 2 a

D xy D (x, y) z = f(x, y) f D (2 ) (x, y, z) f R z = 1 x 2 y 2 {(x, y); x 2 +y 2 1} x 2 +y 2 +z 2 = 1 1 z (x, y) R 2 z = x 2 y

2 (2016 3Q N) c = o (11) Ax = b A x = c A n I n n n 2n (A I n ) (I n X) A A X A n A A A (1) (2) c 0 c (3) c A A i j n 1 ( 1) i+j A (i, j) A (i, j) ã i

No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2

6. Euler x

1W II K =25 A (1) office(a439) (2) A4 etc. 12:00-13:30 Cafe David 1 2 TA appointment Cafe D

.1 A cos 2π 3 sin 2π 3 sin 2π 3 cos 2π 3 T ra 2 deta T ra 2 deta T ra 2 deta a + d 2 ad bc a 2 + d 2 + ad + bc A 3 a b a 2 + bc ba + d c d ca + d bc +

S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t

1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3

さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n


f : R R f(x, y) = x + y axy f = 0, x + y axy = 0 y 直線 x+y+a=0 に漸近し 原点で交叉する美しい形をしている x +y axy=0 X+Y+a=0 o x t x = at 1 + t, y = at (a > 0) 1 + t f(x, y

A_chapter3.dvi

) Binary Cubic Forms / 25

0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (,

2.4 ( ) ( B ) A B F (1) W = B A F dr. A F q dr f(x,y,z) A B Γ( ) Minoru TANAKA (Osaka Univ.) I(2011), Sec p. 1/30

1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

φ s i = m j=1 f x j ξ j s i (1)? φ i = φ s i f j = f x j x ji = ξ j s i (1) φ 1 φ 2. φ n = m j=1 f jx j1 m j=1 f jx j2. m

振動と波動

untitled

( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a

D 24 D D D

4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ

6.1 (P (P (P (P (P (P (, P (, P.101

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

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.

n ( (

ρ ( ) sgv + ρwgv γ sv + γ wv γ s + γ w e e γ ρ g s s γ s ( ) + γ w( ) Vs + V Vs + V + e + e + e γ γ sa γ e e n( ) + e γ γ s ( n) + γ wn γ s, γ w γ γ +

?

, = = 7 6 = 42, =

Note.tex 2008/09/19( )

S K(S) = T K(T ) T S K n (1.1) n {}}{ n K n (1.1) 0 K 0 0 K Q p K Z/pZ L K (1) L K L K (2) K L L K [L : K] 1.1.

Transcription:

.. 3. 3 3. 3 4 3. 5 6 3 7 3.3 9 4. 9 0 6 3 7 0705

φ c d φ d., φ cd, φd. ) O x s + b l cos s s c l / q taφ / q taφ / c l / X + X E + C l w q B s E q q ul q q ul w w q q E E + E E + ul X X + (a) (b) (c) X X + BC σ q / l q BC BC q ( + σ taφ ) + u taφ l s σ σ u u, φ l ()

ls ta { l + ( q ul) φ } M o 0 wx s l q wx ws ws { l + ( q ul) taφ } { l + ( q ul) taφ } ( l + taφ ) q + (3) {( w + E E+ ) cos ( X X ) s} 0 wx wx { l + {( w + E E ) cos ( X X ) s ul}taφ } + [ l + ( wcos ul) taφ + {( E E ) cos ( X X ) s}taφ ] + {( E ) cos ( ) s }ta E+ X X φ 0 + ta wx [ l + ( wcos ul) φ ] x s l + ( wcos ul) taφ ws [ ] + + () (3) (4) (5) (6) q q ul taφ l w + E cos cos E+ ul q q s s 0 w + E q E l( u cos s + + / ) cos + s taφ / (6.33) l bsec, x s (6) w w s s [ b + {( w ul cos) + ( E E )}taφ ] + + ta taφ / l cos + {( w ul cos) + ( E E cos + s taφ / + sec )}taφ E + 0 E w s l cos + ( w ul cos) taφ s taφ w cos + s b + ( w ub) taφ ta taφ cos + (7) (8) (9) (a) l BC BC u

3 w φ φ CU σ u (3) ) (3)q q ul X X + q wcos q wcos ul (6) u0 q wcos c, φ (3) ( cl + wcos taφ) (0) ws 3. (6) (9) (0) 3. ) W W W s τ τ W s / l σ W W cos σ W cos / l s c, φ W cos s c + σ taφ c + taφ (kn/m ) l Στ l Σs l s Σs l Σ( cl + W cos taφ) s (0) Στ l ΣW s

4 O(a,b) x Rs O A ( h + hh h + h G 3 h + h +) h+ h+ b θ b x Rcos O - y b R ( x a) xx + W γ A h h + W cos l W s s l cl + W cos taφ γ t c φ (0) W W A (kn) γ t A(m )γ t (kn/m 3 ) ( γ ) 8m 45 c0kn/m φ 5 γ t 8 kn/m 3 3 s 9 p7. B(x b,y b )(0,0), C(x c,y c )(0.05,8). O BC G x a y 8.3 θ 74 m 0. B(x b,y b )(0,0) B. C(x c,y c )(.05,8) BCDx c CHy c β 45 36 3. BC ym xm y c /x c 0.7398 3 4. BC G(x g,y g )(x c /,y c /)(5.53,4) 5. GO ym x+ m m m x c /y c.38 (x c +y c )/(y c ).63 6. O(a,b)a0.7 5 b.40 DEa 7. R(CE +OE ) 0.5 CEx c aoeby c R.40 8. CBtaC/Bacta(C/B)0.6664ad35.90 9. BC BC(x c +y c ) 0.5 3.64 0. θ 90 accos( BC / R) accos ( BC / R) 0.9940ad 36.75. (x-a) +(y-b) R. BA ymx45 m yx 3. AC yy c O D E R.4m G A.05m C H8m

5 4. xx (,,3,,)x,, 3, 4, 5, 6, 7, 8, 9, 0,.05 h + h+ 5. A ( h + hh+ ) b x0 3 h + h + y b R ( x a) 6..8ad 7. c l c R θ 9. 48 l R θ 4. 6 ( cl + W cos taφ) 8. s. 36 W s No. () () (3) (4) (5) (6) (7) (8) (9) (0) () () (3) 0.03 0.97 0.49 0.50 8.74 0.04 0.00.40.00 0.38 8.73 0.5.85.4.38 5.4 0. 0.06.34 0.99 3.09 5.7 3 3 3 0.36.64.5.36 40.47 0. 0..9 0.98 8.38 39.7 4 4 4 0.66 3.34.99 3.35 53.84 0.9 0.45 0.95 0.96 5.83 5.70 5 5 5.07 3.93 3.63 4.36 65.38 0.38 0.79 0.6 0.93 4.9 60.83 6 6 6.60 4.40 4.6 5.34 74.9 0.47.4 0.6 0.89 35.0 66.75 7 7 7.7 4.7 4.56 6.34 8. 0.56.8 9.59 0.84 45.65 69.05 8 8 8 3. 4.89 4.8 7.33 86.5 0.64.53 8.87 0.78 55.65 67.8 9 9 8 4.9 3.8 4.35 8.3 78.5 0.73 3.4 7.98 0.70 57.05 54.77 0 0 8 5.63.37 3.09 9.9 55.63 0.8 4.56 6.83 0.60 45.35 33.35.05 8 8.00 0.00.5 0.8.4 0.89 5.95 5.45 0.48 0.0 0.7 3.4 488.8 () xx (m) () BAAC y (m) (3) y (m) (4) ()(3) (5) A(m ) (6) O x(m) (7) W(kN) (8) sx/r (9) y (0) y( y b)(9) () cosy/r () Ws (3) Wcos ) 3. (9) O O O O x y

6 x y 4 y 50m,3 B,A 0 8 6 0 4 8 3 40 48m x 8 0 6 0 4 3 4 8 3m y 4 4 0 0.0 0.0 8.0 40.0 8.0 8.0 0.0 0.0 0.0 0.0 0.0 50.0 50.0 50.0 50.0 50.0 0.0 5.0 8.0 6.0 4.0 8.0 0.0 () x N N () x (3) y x N (4) N (5) y x (6) N (7) x x a xx b (8) y y a xy b (BISHOP) 4 0 3 4 X (m).00 0.00 8.00 40.00 Y (m) 8.00 8.00 0.00 0.00 (m) 50.00 50.00 50.00 50.00 (kn).00.00.00 C(kN/m) () (kn/m3) 0.000 5.0 8.00

7 X 6.00m 4.00m Y 8.00m 0.00m XY) ( 0.75m, 6.63m) R.37m.374 3 3) 40.65.00.65.00.70 0.70 0 0 6 8 5 O x R 8 0.0m.0m () () 9.6 kn/m 3 4.0m (3) φ 30 y (kn/m ) (kn/m 3 ) () 9.6 0.0.6 () 9.6 0.0 5.40 (3) 0.00 30.0 9.8 5 3

8 (BISHOP) 6 3 40

9 3 4 5 6 X (m).00 0.00.00 6.00 8.00 5.00 Y (m) 4.00 4.00 3.00.00 0.00 0.00 Y (m) 4.00 4.00 3.00.00.00.00 Y (m) 3 4.00 4.00 3.00 3.00 3.00 3.00 (m).00.00.00.00.00.00 (kn).00.00.00.00.00 C(kN/m) () ( kn/m3) 9.60.0.6 9.60.0 5.40 3.000 30.0 9.8 X.00m 6.00m Y.00m 8.00m XY) (.7m, 3.08m) R.90m.63 3.3 p.7 3

0 4. 3 3 3 ) 00 ) 004 3) 葥 p.000 ) 3 007//05

2024 © docsplayer.net プライバシー | 利用規約 | フィードバック