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1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2

1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2

時系列解析

B L12(2016-07-11 Mon) : Time-stamp: 2016-07-11 Mon 17:25 JST hig,, Excel,. http://hig3.net ( ) L12 B(2016) 1 / 24 L11-Q1 Quiz : 1 E[R] = 1 2, V[R] = 9 12 = 3 4. R(t), E[X(30)] = E[X(0)] + 30 1 2 = 115,

.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0,

.1.1 Y K L Y = K 1 3 L 3 L K K (K + ) 1 1 3 L 3 K 3 L 3 K 0 (K + K) 1 3 L 3 K 1 3 L 3 lim K 0 K = L (K + K) 1 3 K 1 3 3 lim K 0 K = 1 3 K 3 L 3 z = f(x, y) x y z x-y-z.1 z = e x +xy y 3 x-y ( ) z 0 f(x,

x ( ) x dx = ax

x ( ) x dx = ax 1 dx = a x log x = at + c x(t) = e at C (C = e c ) a > 0 t a < 0 t 0 (at + b ) h dx = lim x(t + h) x(t) h 0 h x(t + h) x(t) h x(t) t x(t + h) x(t) ax(t) h x(t + h) x(t) + ahx(t) 0, h, 2h,

OCAMI

OCAMI 2015 12 16 1. 2. R 3. Lie 4. U(n), SU(n), O(n), SO(n), Sp(n) 5. U(n), SU(n), O(n), SO(n), Sp(n) 6. Lie 7. G 2 G 2 /SO(4) 1. M Riemann M Riemann def x M, s x : s.t. s 2 x = id, x s x s x x R n S n

平成 22 年度 ( 第 32 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 ~8 22 月年 58 日開催月 2 日 ) V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2

3 90 2006 1. V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2 = xz y 2 = 0} V (x,y) n = 1 n = 2 (x,y) V n = 1 n = 2 (3/5,4/5),(5/13,12/13)... n 3 V (0,±1),(±1,0) ( ) n 3 x n + y n = z n,

limit&derivative

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II (1 4 ) 1. p.13 1 (x, y) (a, b) ε(x, y; a, b) 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 x a A = f x (a, b) y x 3 3y 3 (x, y) (, ) f (x, y) = x + y (x, y) = (, )

40 6 y mx x, y 0, 0 x 0. x,y 0,0 y x + y x 0 mx x + mx m + m m 7 sin y x, x x sin y x x. x sin y x,y 0,0 x 0. 8 x r cos θ y r sin θ x, y 0, 0, r 0. x,

9.. x + y + 0. x,y, x,y, x r cos θ y r sin θ xy x y x,y 0,0 4. x, y 0, 0, r 0. xy x + y r 0 r cos θ sin θ r cos θ sin θ θ 4 y mx x, y 0, 0 x 0. x,y 0,0 x x + y x 0 x x + mx + m m x r cos θ 5 x, y 0, 0,

II

II 16 16.0 2 1 15 x α 16 x n 1 17 (x α) 2 16.1 16.1.1 2 x P (x) P (x) = 3x 3 4x + 4 369 Q(x) = x 4 ax + b ( ) 1 P (x) x Q(x) x P (x) x P (x) x = a P (a) P (x) = x 3 7x + 4 P (2) = 2 3 7 2 + 4 = 8 14 +

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

2009 9 6 16 7 1 7.1 1 1 1 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(cos y y sin y) y dy 1 sin

(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n

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7-12.dvi

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E9A40JD_001_029.qx4j

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190 法律学研究 56 号 (2016)

189 労働者に対する使用者の損害賠償請求 責任制限法理の再検討 藤田大幹 ( 内藤研究会 4 年 ) 1 2 3 1 2 3 1 2 3 1 2 2013 9 3 5111 82 4189 36 190 法律学研究 56 号 (2016) 4 5 6 6 16 715 3 7 1960 70 191 2000 8 1 715 3 9 10 11 12 100 13 14 15 192 法律学研究

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10 DRAMLSI 20 10 631 1 3 4

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stat2_slides-13.key

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

Akito Tsuboi June 22, 2006 1 T ϕ T M M ϕ M M ϕ T ϕ 2 Definition 1 X, Y, Z,... 1 1. X, Y, Z,... 2. A, B (A), (A) (B), (A) (B), (A) (B) Exercise 2 1. (X) (Y ) 2. ((X) (Y )) (Z) 3. (((X) (Y )) (Z)) Exercise

2009 : M (CG)

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9 E B 9.1 9.1.1 Ampère Ampère Ampère s law B S µ 0 B ds = µ 0 j ds (9.1) S rot B = µ 0 j (9.2) S Ampère Biot-Savart oulomb Gauss Ampère rot B 0 Ampère µ 0 9.1 (a) (b) I B ds = µ 0 I. I 1 I 2 B ds = µ 0

DVIOUT

A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)

Acrobat Distiller, Job 128

(2 ) 2 < > ( ) f x (x, y) 2x 3+y f y (x, y) x 2y +2 f(3, 2) f x (3, 2) 5 f y (3, 2) L y 2 z 5x 5 ` x 3 z y 2 2 2 < > (2 ) f(, 2) 7 f x (x, y) 2x y f x (, 2),f y (x, y) x +4y,f y (, 2) 7 z (x ) + 7(y 2)

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lecture

149 6 6.1 y(x) x = x =1 1+y (x) 2 dx. y(x) 6.1 ( ). xy y (, ) (b, B) y (b, B) y(x) O B y mg (x, y(x)) y(x) 6.1: g m y(x) v =mv 2 /2 mgy(x) v = 2gy(x) 1+y (x) 2 dx 2gy(x) y() =, y(b) =B b x 15 y 6 6.2 (

73

73 74 ( u w + bw) d = Ɣ t tw dɣ u = N u + N u + N 3 u 3 + N 4 u 4 + [K ] {u = {F 75 u δu L σ (L) σ dx σ + dσ x δu b δu + d(δu) ALW W = L b δu dv + Aσ (L)δu(L) δu = (= ) W = A L b δu dx + Aσ (L)δu(L) Aσ

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

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