( ) a C n ( R n ) R a R C n. a C n (or R n ) a 0 2. α C( R ) a C n αa = α a 3. a, b C n a + b a + b ( ) p 8..2 (p ) a = [a a n ] T C n p n a

Erased_PDF.pdf

数学概論I

{a n } M >0 s.t. a n 5 M for n =1, 2,... lim n a n = α ε =1 N s.t. a n α < 1 for n > N. n > N a n 5 a n α + α < 1+ α. M := max{ a 1,..., a N, 1+ α } a n 5 M ( n) 1 α α 1+ α t a 1 a N+1 a N+2 a 2 1 a n

卓球の試合への興味度に関する確率論的分析

17 i 1 1 1.1..................................... 1 1.2....................................... 1 1.3..................................... 2 2 5 2.1................................ 5 2.2 (1).........................

n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m

1 1 1 + 1 4 + + 1 n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m a n < ε 1 1. ε = 10 1 N m, n N a m a n < ε = 10 1 N

a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552

3 3.0 a n a n ( ) () a m a n = a m+n () (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 55 3. (n ) a n n a n a n 3 4 = 8 8 3 ( 3) 4 = 8 3 8 ( ) ( ) 3 = 8 8 ( ) 3 n n 4 n n

_0212_68<5A66><4EBA><79D1>_<6821><4E86><FF08><30C8><30F3><30DC><306A><3057><FF09>.pdf

koji07-02.dvi

007 I II III 1,, 3, 4, 5, 6, 7 5 4 1 ε-n 1 ε-n ε-n ε-n. {a } =1 a ε N N a a N= a a

² ² ² ²

² ² ² ² n=44 n =44 n=44 n=44 20.5% 22.7% 13.6% 27.3% 54.5% 25.0% 59.1% 18.2% 70.5% 15.9% 47.7% 25.0% 60% 40% 20% 0% n=44 52.3% 27.3% 11.4% 6.8% 27.55.5 306 336.6 408 n=44 9.1% 6.8% n=44 6.8% 2.3% 31.8%

資料5：聖ウルスラ学院英智小・中学校　提出資料（1）

ε

２００７年０８月号　０２２４１６／０８１２　会告

³ÎΨÏÀ

2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p

31 4 MATLAB A, B R 3 3 A = , B = mat_a, mat_b >> mat_a = [-1, -2, -3; -4, -5, -6; -7, -8, -9] mat_a =

3 4 MATLAB 3 4. A, B R 3 3 2 3 4 5 6 7 8 9, B = mat_a, mat_b >> mat_a = [-, -2, -3; -4, -5, -6; -7, -8, -9] 9 8 7 6 5 4 3 2 mat_a = - -2-3 -4-5 -6-7 -8-9 >> mat_b = [-9, -8, -7; -6, -5, -4; -3, -2, -]

20 9 19 1 3 11 1 3 111 3 112 1 4 12 6 121 6 122 7 13 7 131 8 132 10 133 10 134 12 14 13 141 13 142 13 143 15 144 16 145 17 15 19 151 1 19 152 20 2 21 21 21 211 21 212 1 23 213 1 23 214 25 215 31 22 33

() Remrk I = [0, ] [x i, x i ]. (x : ) f(x) = 0 (x : ) ξ i, (f) = f(ξ i )(x i x i ) = (x i x i ) = ξ i, (f) = f(ξ i )(x i x i ) = 0 (f) 0.

() 6 f(x) [, b] 6. Riemnn [, b] f(x) S f(x) [, b] (Riemnn) = x 0 < x < x < < x n = b. I = [, b] = {x,, x n } mx(x i x i ) =. i [x i, x i ] ξ i n (f) = f(ξ i )(x i x i ) i=. (ξ i ) (f) 0( ), ξ i, S, ε >

(ii) (iii) z a = z a =2 z a =6 sin z z a dz. cosh z z a dz. e z dz. (, a b > 6.) (z a)(z b) 52.. (a) dz, ( a = /6.), (b) z =6 az (c) z a =2 53. f n (z

B 4 24 7 9 ( ) :,..,,.,. 4 4. f(z): D C: D a C, 2πi C f(z) dz = f(a). z a a C, ( ). (ii), a D, a U a,r D f. f(z) = A n (z a) n, z U a,r, n= A n := 2πi C f(ζ) dζ, n =,,..., (ζ a) n+, C a D. (iii) U a,r

日本内科学会雑誌第102巻第4号

u = u(t, x 1,..., x d ) : R R d C λ i = 1 := x 2 1 x 2 d d Euclid Laplace Schrödinger N := {1, 2, 3,... } Z := {..., 3, 2, 1,, 1, 2, 3

2 2 1 5 5 Schrödinger i u t + u = λ u 2 u. u = u(t, x 1,..., x d ) : R R d C λ i = 1 := 2 + + 2 x 2 1 x 2 d d Euclid Laplace Schrödinger 3 1 1.1 N := {1, 2, 3,... } Z := {..., 3, 2, 1,, 1, 2, 3,... } Q

untitled

1 1 Ax = b A R m m A b R m x R m A shift-and invert Lanczos - LU CG A = LU LU Ly = b Ux = y A LU A A = LL T 1 LU b,, Vol. 11, No. 4, pp. 14 18 (2006). x * x (0), x (1), x (2), A Ap A # x (n+1) = Cx (n)

numb.dvi

11 Poisson kanenko@mbkniftycom alexeikanenko@docomonejp http://wwwkanenkocom/ , u = f, ( u = u+f u t, u = f t ) 1 D R 2 L 2 (D) := {f(x,y) f(x,y) 2 dxdy < )} D D f,g L 2 (D) (f,g) := f(x,y)g(x,y)dxdy (L

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()

03337-010-001.PDF

π, R { 2, 0, 3} , ( R),. R, [ 1, 1] = {x R 1 x 1} 1 0 1, [ 1, 1],, 1 0 1,, ( 1, 1) = {x R 1 < x < 1} [ 1, 1] 1 1, ( 1, 1), 1, 1, R A 1

sup inf (ε-δ 4) 2018 1 9 ε-δ,,,, sup inf,,,,,, 1 1 2 3 3 4 4 6 5 7 6 10 6.1............................................. 11 6.2............................... 13 1 R R 5 4 3 2 1 0 1 2 3 4 5 π( R) 2 1 0

2 2 MATHEMATICS.PDF 200-2-0 3 2 (p n ), ( ) 7 3 4 6 5 20 6 GL 2 (Z) SL 2 (Z) 27 7 29 8 SL 2 (Z) 35 9 2 40 0 2 46 48 2 2 5 3 2 2 58 4 2 6 5 2 65 6 2 67 7 2 69 2 , a 0 + a + a 2 +... b b 2 b 3 () + b n a

01

2 0 0 7 0 3 2 2 i n d e x 0 7. 0 2. 0 3. 0 4. 0 8. 0 9. 1 0. 1 1. 0 5. 1 2. 1 3. 1 4. 1 5. 1 6. 1 7. 1 8. 1 9. 2 0. 2 1. 2 3. 2 4. 2 5. 2 6. O k h o t s k H a m a n a s u B e e f 0 2 http://clione-beef.n43.jp

301-A2.pdf

301 21 1 (1),, (3), (4) 2 (1),, (3), (4), (5), (6), 3,?,?,??,?? 4 (1)!?, , 6 5 2 5 6 1205 22 1 (1) 60 (3) (4) (5) 2 (1) (3) (4) 3 (1) (3) (4) (5) (6) 4 (1) 5 (1) 6 331 331 7 A B A B A B A 23 1 2 (1) (3)

No. 1261 2003. 4. 9 14 14 14 14 15 30 21 19 150 35 464 37 38 40 20 970 90 80 90 181130 a 151731 48 11 151731 42 44 47 63 12 a 151731 47 10 11 16 2001 11000 11 2002 10 151731 46 5810 2795195261998 151731

r

73 29 2008 200 4 416 2008 20 042 0932 10 1977 200 1 2 3 4 5 7 8 9 11 12 14 15 16 17 18 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 200r 11 1 1 1 1 700200 200

1 I

1 I 3 1 1.1 R x, y R x + y R x y R x, y, z, a, b R (1.1) (x + y) + z = x + (y + z) (1.2) x + y = y + x (1.3) 0 R : 0 + x = x x R (1.4) x R, 1 ( x) R : x + ( x) = 0 (1.5) (x y) z = x (y z) (1.6) x y =

2010 IA ε-n I 1, 2, 3, 4, 5, 6, 7, 8, ε-n 1 ε-n ε-n? {a n } n=1 1 {a n } n=1 a a {a n } n=1 ε ε N N n a n a < ε

00 IA ε-n I,, 3, 4, 5, 6, 7, 8, 9 4 6 ε-n ε-n ε-n? {a } = {a } = a a {a } = ε ε N N a a < ε ε-n ε ε N a a < ε N ε ε N ε N N ε N [ > N = a a < ε] ε > 0 N N N ε N N ε N N ε a = lim a = 0 ε-n 3 ε N 0 < ε

(1) θ a = 5(cm) θ c = 4(cm) b = 3(cm) (2) ABC A A BC AD 10cm BC B D C 99 (1) A B 10m O AOB 37 sin 37 = cos 37 = tan 37

4. 98 () θ a = 5(cm) θ c = 4(cm) b = (cm) () D 0cm 0 60 D 99 () 0m O O 7 sin 7 = 0.60 cos 7 = 0.799 tan 7 = 0.754 () xkm km R km 00 () θ cos θ = sin θ = () θ sin θ = 4 tan θ = () 0 < x < 90 tan x = 4 sin

s s U s L e A = P A l l + dl dε = dl l l

P (ε) A o B s= P A s B o Y l o s Y l e = l l 0.% o 0. s e s B 1 s (e) s Y s s U s L e A = P A l l + dl dε = dl l l ε = dε = l dl o + l lo l = log l o + l =log(1+ e) l o Β F Α E YA C Ο D ε YF B YA A YA

December 28, 2018

e-mail : kigami@i.kyoto-u.ac.jp December 28, 28 Contents 2............................. 3.2......................... 7.3..................... 9.4................ 4.5............. 2.6.... 22 2 36 2..........................

20 6 4 1 4 1.1 1.................................... 4 1.1.1.................................... 4 1.1.2 1................................ 5 1.2................................... 7 1.2.1....................................

untitled

,, 2 2.,, A, PC/AT, MB, 5GB,,,, ( ) MB, GB 2,5,, 8MB, A, MB, GB 2 A,,,? x MB, y GB, A (), x + 2y () 4 (,, ) (hanba@eee.u-ryukyu.ac.jp), A, x + 2y() x y, A, MB ( ) 8 MB ( ) 5GB ( ) ( ), x x x 8 (2) y y

平成20年5月 協会創立50年の歩み　海の安全と環境保全を目指して 友國八郎 海上保安庁 長官 岩崎貞二 日本船主協会 会長 前川弘幸 JF全国漁業協同組合連合会 代表理事会長 服部郁弘 日本船長協会 会長 森本靖之 日本船舶機関士協会 会長 大内博文 航海訓練所 練習船船長 竹本孝弘 第二管区海上保安本部長 梅田宜弘

ａｐｈｐ３７－１１＿プロ１／ｋｙ８６９５４３５４０４１０００５５９０

Œ{Ł¶/1ŒÊ −ªfiª„¾ [ 1…y†[…W ]

本文／扉１

プログラム

Program

日本内科学会雑誌第96巻第11号

29

9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n

海生研ニュース

プログラム

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π

4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan

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

Part2 47 Example 161 93 1 T a a 2 M 1 a 1 T a 2 a Point 1 T L L L T T L L T L L L T T L L T detm a 1 aa 2 a 1 2 + 1 > 0 11 T T x x M λ 12 y y x y λ 2 a + 1λ + a 2 2a + 2 0 13 D D a + 1 2 4a 2 2a + 2 a

I , : ~/math/functional-analysis/functional-analysis-1.tex

I 1 2004 8 16, 2017 4 30 1 : ~/math/functional-analysis/functional-analysis-1.tex 1 3 1.1................................... 3 1.2................................... 3 1.3.....................................

> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3

13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >

広報みはま.indd

1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1

sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω ω α 3 3 2 2V 3 33+.6T m T 5 34m Hz. 34 3.4m 2 36km 5Hz. 36km m 34 m 5 34 + m 5 33 5 =.66m 34m 34 x =.66 55Hz, 35 5 =.7 485.7Hz 2 V 5Hz.5V.5V V

さくらの個別指導 ( さくら教育研究所 ) a a n n A m n 1 a m a n = a m+n 2 (a m ) n = a mn 3 (ab) n = a n b n a n n = = 3 2, = 3 2+

5 5. 5.. a a n n A m n a m a n = a m+n (a m ) n = a mn 3 (ab) n = a n b n a n n 0 3 3 0 = 3 +0 = 3, 3 3 = 3 +( ) = 3 0 3 0 3 3 0 = 3 3 =, 3 = 30 3 = 3 0 a 0 a`n a 0 n a 0 = a`n = a n a` = a 83 84 5 5.

z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy

f f x, y, u, v, r, θ r > = x + iy, f = u + iv C γ D f f D f f, Rm,. = x + iy = re iθ = r cos θ + i sin θ = x iy = re iθ = r cos θ i sin θ x = + = Re, y = = Im i r = = = x + y θ = arg = arctan y x e i =

「産業上利用することができる発明」の審査の運用指針（案）

1 1.... 2 1.1... 2 2.... 4 2.1... 4 3.... 6 4.... 6 1 1 29 1 29 1 1 1. 2 1 1.1 (1) (2) (3) 1 (4) 2 4 1 2 2 3 4 31 12 5 7 2.2 (5) ( a ) ( b ) 1 3 2 ( c ) (6) 2. 2.1 2.1 (1) 4 ( i ) ( ii ) ( iii ) ( iv)

取扱説明書

ED-601 ED-501 ED-401 2 3 4 23 14 5 6 18 10 7 1 2 6 3 4 8 9 16 16 16 12 1 2 18 10 2 1 5 12 11 1 2 1 2 12 1 2 13 16 14 3 2 4 1 1 2 16 3 4 18 15 1 2 16 2 3 1 1 2 3 18 17 18 22 19 D A C 20 A B 22 B C D 22

.V...z.\

201604_建築総合_2_架橋ポリ-ポリブテン_cs6.indd

1 R n (x (k) = (x (k) 1,, x(k) n )) k 1 lim k,l x(k) x (l) = 0 (x (k) ) 1.1. (i) R n U U, r > 0, r () U (ii) R n F F F (iii) R n S S S = { R n ; r > 0

III 2018 11 7 1 2 2 3 3 6 4 8 5 10 ϵ-δ http://www.mth.ngoy-u.c.jp/ ymgmi/teching/set2018.pdf http://www.mth.ngoy-u.c.jp/ ymgmi/teching/rel2018.pdf n x = (x 1,, x n ) n R n x 0 = (0,, 0) x = (x 1 ) 2 +

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 =

1 1.1 ( ). z = + bi,, b R 0, b 0 2 + b 2 0 z = + bi = ( ) 2 + b 2 2 + b + b 2 2 + b i 2 r = 2 + b 2 θ cos θ = 2 + b 2, sin θ = b 2 + b 2 2π z = r(cos θ + i sin θ) 1.2 (, ). 1. < 2. > 3. ±,, 1.3 ( ). A

Trapezoidal Rule θ = 1/ x n x n 1 t = 1 [f(t n 1, x n 1 ) + f(t n, x n )] (6) 1. dx dt = f(t, x), x(t 0) = x 0 (7) t [t 0, t 1 ] f t [t 0, t 1 ], x x

University of Hyogo 8 8 1 d x(t) =f(t, x(t)), dt (1) x(t 0 ) =x 0 () t n = t 0 + n t x x n n x n x 0 x i i = 0,..., n 1 x n x(t) 1 1.1 1 1 1 0 θ 1 θ x n x n 1 t = θf(t n 1, x n 1 ) + (1 θ)f(t n, x n )

6 ( ) 1 / 53

6 / 6 (2014 11 05 ) / 53 6 (2014 11 05 ) 1 / 53 nodeedge 2 u v u v (u, v) 6 (2014 11 05 ) 2 / 53 Twitter 6 (2014 11 05 ) 3 / 53 Facebook 6 (2014 11 05 ) 4 / 53 N N N 1,2,..., N (i, j )i j 10 i j 2(i, j

r 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B

1 1.1 1 r 1 m A r/m i) t ii) m i) t Bt; m) Bt; m) = A 1 + r ) mt m ii) Bt; m) Bt; m) = A 1 + r ) mt m { = A 1 + r ) m } rt r m n = m r m n Bt; m) Aert e lim 1 + 1 n 1.1) n!1 n) e a 1, a 2, a 3,... {a n

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

22 A 3,4 No.3 () (2) (3) (4), (5) (6) (7) (8) () n x = (x,, x n ), = (,, n ), x = ( (x i i ) 2 ) /2 f(x) R n f(x) = f() + i α i (x ) i + o( x ) α,, α n g(x) = o( x )) lim x g(x) x = y = f() + i α i(x )

EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編

K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D

untitled

ありがとうございました

- 1 - - 2 - - 3 - - 4 - - 5 - 1 2 AB C A B C - 6 - - 7 - - 8 - 10 1 3 1 10 400 8 9-9 - 2600 1 119 26.44 63 50 15 325.37 131.99 457.36-10 - 5 977 1688 1805 200 7 80-11 - - 12 - - 13 - - 14 - 2-1 - 15 -

EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編

K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D

公務員人件費のシミュレーション分析

47 50 (a) (b) (c) (7) 11 10 2018 20 2028 16 17 18 19 20 21 22 20 90.1 9.9 20 87.2 12.8 2018 10 17 6.916.0 7.87.4 40.511.6 23 0.0% 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2.0% 4.0% 6.0% 8.0%

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 A B (A/B) 1 1,185 17,801 6.66% 2 943 26,598 3.55% 3 3,779 112,231 3.37% 4 8,174 246,350 3.32% 5 671 22,775 2.95% 6 2,606 89,705 2.91% 7 738 25,700 2.87% 8 1,134

橡hashik-f.PDF

1 1 1 11 12 13 2 2 21 22 3 3 3 4 4 8 22 10 23 10 11 11 24 12 12 13 25 14 15 16 18 19 20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 144 142 140 140 29.7 70.0 0.7 22.1 16.4 13.6 9.3 5.0 2.9 0.0

198

197 198 199 200 201 202 A B C D E F G H I J K L 203 204 205 A B 206 A B C D E F 207 208 209 210 211 212 213 214 215 A B 216 217 218 219 220 221 222 223 224 225 226 227 228 229 A B C D 230 231 232 233 A

ネットショップ・オーナー２ ユーザーマニュアル

1 1-1 1-2 1-3 1-4 1 1-5 2 2-1 A C 2-2 A 2 C D E F G H I 2-3 2-4 2 C D E E A 3 3-1 A 3 A A 3 3 3 3-2 3-3 3-4 3 C 4 4-1 A A 4 B B C D C D E F G 4 H I J K L 4-2 4 C D E B D C A C B D 4 E F B E C 4-3 4

1

1 2 3 4 5 (2,433 ) 4,026 2710 243.3 2728 402.6 6 402.6 402.6 243.3 7 8 20.5 11.5 1.51 0.50.5 1.5 9 10 11 12 13 100 99 4 97 14 A AB A 12 14.615/100 1.096/1000 B B 1.096/1000 300 A1.5 B1.25 24 4,182,500

新婚世帯家賃あらまし

05[ ]戸田(責)村.indd

147 2 62 4 3.2.1.16 3.2.1.17 148 63 1 3.2.1.F 3.2.1.H 3.1.1.77 1.5.13 1 3.1.1.05 2 3 4 3.2.1.20 3.2.1.22 3.2.1.24 3.2.1.D 3.2.1.E 3.2.1.18 3.2.1.19 2 149 3.2.1.23 3.2.1.G 3.1.1.77 3.2.1.16 570 565 1 2

/9/ ) 1) 1 2 2) 4) ) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x ) x 2 8x + 10 = 0

1. 2018/9/ ) 1) 8 9) 2) 6 14) + 14 ) 1 4 8a 8b) 2 a + b) 4) 2 : 7 = x 8) : x ) x ) + 1 2 ) + 2 6) x + 1)x + ) 15 2. 2018/9/ ) 1) 1 2 2) 4) 2 + 6 5) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x 2 15 12

lecture

5 3 3. 9. 4. x, x. 4, f(x, ) :=x x + =4,x,.. 4 (, 3) (, 5) (3, 5), (4, 9) 95 9 (g) 4 6 8 (cm).9 3.8 6. 8. 9.9 Phsics 85 8 75 7 65 7 75 8 85 9 95 Mathematics = ax + b 6 3 (, 3) 3 ( a + b). f(a, b) ={3 (a

,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = , ( ) : = F 1 + F 2 + F 3 + ( ) : = i Fj j=1 2

6 2 6.1 2 2, 2 5.2 R 2, 2 (R 2, B, µ)., R 2,,., 1, 2, 3,., 1, 2, 3,,. () : = 1 + 2 + 3 + (6.1.1).,,, 1 ,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = 1 + 2 + 3 +,

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

70の法則

70 70 1 / 27 70 1 2 3 4 5 6 2 / 27 70 70 70 X r % = 70 2 r r r 10 72 70 72 70 : 1, 2, 5, 7, 10, 14, 35, 70 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 3 / 27 r = 10 70 r = 10 70 1 : X, X 10 = ( X + X

A11 (1993,1994) 29 A12 (1994) 29 A13 Trefethen and Bau Numerical Linear Algebra (1997) 29 A14 (1999) 30 A15 (2003) 30 A16 (2004) 30 A17 (2007) 30 A18

2013 8 29y, 2016 10 29 1 2 2 Jordan 3 21 3 3 Jordan (1) 3 31 Jordan 4 32 Jordan 4 33 Jordan 6 34 Jordan 8 35 9 4 Jordan (2) 10 41 x 11 42 x 12 43 16 44 19 441 19 442 20 443 25 45 25 5 Jordan 26 A 26 A1

IA 2013 : :10722 : 2 : :2 :761 :1 (23-27) : : ( / ) (1 /, ) / e.g. (Taylar ) e x = 1 + x + x xn n! +... sin x = x x3 6 + x5 x2n+1 + (

IA 2013 : :10722 : 2 : :2 :761 :1 23-27) : : 1 1.1 / ) 1 /, ) / e.g. Taylar ) e x = 1 + x + x2 2 +... + xn n! +... sin x = x x3 6 + x5 x2n+1 + 1)n 5! 2n + 1)! 2 2.1 = 1 e.g. 0 = 0.00..., π = 3.14..., 1

A A = a 41 a 42 a 43 a 44 A (7) 1 (3) A = M 12 = = a 41 (8) a 41 a 43 a 44 (3) n n A, B a i AB = A B ii aa

1 2 21 2 2 [ ] a 11 a 12 A = a 21 a 22 (1) A = a 11 a 22 a 12 a 21 (2) 3 3 n n A A = n ( 1) i+j a ij M ij i =1 n (3) j=1 M ij A i j (n 1) (n 1) 2-1 3 3 A A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33

I z n+1 = zn 2 + c (c ) c pd L.V. K. 2

I 2012 00-1 I : October 1, 2012 Version : 1.1 3. 10 1 10 15 10 22 1: 10 29 11 5 11 12 11 19 2: 11 26 12 3 12 10 12 17 3: 12 25 1 9 1 21 3 1 I 2012 00-2 z n+1 = zn 2 + c (c ) c http://www.math.nagoya-u.ac.jp/~kawahira/courses/12w-tenbou.html

/02/18

3 09/0/8 i III,,,, III,?,,,,,,,,,,,,,,,,,,,,?,?,,,,,,,,,,,,,,!!!,? 3,,,, ii,,,!,,,, OK! :!,,,, :!,,,,,, 3:!,, 4:!,,,, 5:!,,! 7:!,,,,, 8:!,! 9:!,,,,,,,,, ( ),, :, ( ), ( ), 6:!,,, :... : 3 ( )... iii,,

(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

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

35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 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

Microsoft Word - 触ってみよう、Maximaに2.doc

i i e! ( x +1) 2 3 ( 2x + 3)! ( x + 1) 3 ( a + b) 5 2 2 2 2! 3! 5! 7 2 x! 3x! 1 = 0 ",! " >!!! # 2x + 4y = 30 "! x + y = 12 sin x lim x!0 x x n! # $ & 1 lim 1 + ('% " n 1 1 lim lim x!+0 x x"!0 x log x

(1) 1 y = 2 = = b (2) 2 y = 2 = 2 = 2 + h B h h h< h 2 h

6 6.1 6.1.1 O y A y y = f() y = f() b f(b) B y f(b) f() = b f(b) f() f() = = b A f() b AB O b 6.1 2 y = 2 = 1 = 1 + h (1 + h) 2 1 2 (1 + h) 1 2h + h2 = h h(2 + h) = h = 2 + h y (1 + h) 2 1 2 O y = 2 1

2 1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a 2 + b 2 α (norm) N(α) = a 2 + b 2 = αα = α 2 α (spure) (trace) 1 1. a R aα =

1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a + b α (norm) N(α) = a + b = αα = α α (spure) (trace) 1 1. a R aα = aα. α = α 3. α + β = α + β 4. αβ = αβ 5. β 0 6. α = α ( ) α = α

8 i, III,,,, III,, :!,,,, :!,,,,, 4:!,,,,,,!,,,, OK! 5:!,,,,,,,,,, OK 6:!, 0, 3:!,,,,! 7:!,,,,,, ii,,,,,, ( ),, :, ( ), ( ), :... : 3 ( )...,, () : ( )..., :,,, ( ), (,,, ),, (ϵ δ ), ( ), (ˆ ˆ;),,,,,,!,,,,.,,

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

6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P

NISTEP REPORT No. 95 ( ) ( ) ( ) ( ) ( ) ( ) 104 397 1022 1050 1173 1674 1738 2679(651cites) 2683 2721 2763 2780 3032 3865 3866 3879 3928 4151 4203 4335 4676 4682 4699 4715 4898 5431