A_chapter3.dvi
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- よいかず わたぬき
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1 : a b c d 2: x x y y 3: x y w (x, y,, w) = (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, ) xȳw (,,, )xȳw (,,, ) xyw, F F = xy w x w xy w xy w xȳ w xy w xy w xȳw xȳw xyw, F F 2 = F = xȳ w xȳ w xy w xȳ w xȳ w xyw F 2 =(x y w)( x y w)(x ȳ w)(x y w)(x y w)( x ȳ w)
2 3.5 n (x,x 2,...,x n ) n, (x,x 2,...,x n )= (c 2,c 3,...,c n) (x,c 2,...,c n ) x c2 2 xc3 3 xcn n., 2 n., 2 n., n, 2 n. 3.6 () = x y x = x xy, = x xy xy =( x)y = y xy, = x y xy. (2) g = xy( w) w( x ȳ) =xy(w ) w(xy ) xy(w ) w(xy ) = g = xyw xy xyw w = xyw xyw xy w = xy w. 3.7 (xy) = () xȳ () xȳ () xy () xy ()xȳ ()xȳ ()xy ()xy = xȳ xy ( ) = xȳ xȳ xy xy xȳ xy = (x y )(x y )(x ȳ )(x ȳ )( x y )( x ȳ ) ( ) = x(y ) =xy x ( ) 2
3 3.8 () n ( ) ( ) ( ) = ( ) ( ) =. n ( ) ( ) = =. (2) x x x x (3) x x = x = x x x =. x = x. (4) (x y)(y )( x) = (xy x yy y)( x) = xy x yy y xxy xx xyy xy = xy xy x x xy xy y y = (5) (a) (x y = x ) (y = ). x x x y = x x y =, x y = x y =. (b) (y = ) (x y = x ). x x y = x. (a), (b) (x y = x ) (y = ). (6) (a) ( = g h) (g = h). = g h, h = g h h = g h h h = g,. (b) (g = h) ( = g h). g = h, h,. g = h g h = h h g h = (a), (b) ( = g h) (g = h). 3
4 (7) = (x a)(x b) =xx xa xb ab = x xa xb ab = (ā b)x ab =(a ) bx ab = x ax bx ab,. (8) = (x y) (y ) =(x y xy) (y y) = x xy y y y = x xy y = x xy y = xȳ ȳ = x(y ) (y ) = x xy y,. (9) xy y x = (xy y xy y) x = (xy y xy) x (xy y xy) = xy y xy x xy xy xy = xy y x, , x =,y =, =,., x (y ) (x y) (x ).. 4: x y y x (y ) x y x (x y) (x ) 3. = x x 2 x 4 x 2 x 3 x 4 (x 2 x 3 x 4 x x 2 x 3 x 4 ), x 4 x 2 x 3 x 4 x x 2 x 3 x 4 (x 2 x 3 x x 2 x 3 ), F.. F = x x 2 x 4 x 2 x 3 x 4 x 4 (x 2 x 3 x x 2 x 3 ) 4
5 x 2 x 4 x 2 3 x 4 x 2 x 3 x 4 x 2 x 3 : (a) = xy x xw y yw w x =,, = y yw w = y w y yw w, y =,,,,. = w = w w = w w = = w w w = w = w = =,. =, = = w, = w = w = = w w =, 2 B. (b) g = x y w (a), g = y w g = y w =ḡ g = w g = w =ḡ g = w g = w =ḡ, 3 B. 5
6 g x x y y y y w w w w 2: 3: 3.2 x < <x n, ROB 2 n, x n+ < <x 2n, 2 n,., (2 n ) 2+2=2 n+. 3.3,g x =, = H(( x =),g( x = )) H(( x =),g( x = )) = H(( x =),g( x = )) =,g x =,,. = H(( x =),g( x = )) H(( x =),g( x = )) = H(( x =),g( x = )) = 3.4., x,x 2,x 3,x 4 = x x 2 x 3 x 4. a b = ā b a b, (x x 2 ) (x 3 x 4 ) = (x x 2 ) (x 3 x 4 ) (x x 2 ) (x 3 x 4 ). 4. 6
7 sw sw2 sw3 sw4 4: 3.4 sw, sw2, sw3, sw4, Lamp , (x,x 2,...,x n )= (c,c 2,...,c n)., = (c,c 2,...,c n) (c,c 2,...,c n )x c xc2 2 xcn n (c,c 2,...,c n )x c xc2 2 xcn n = (,,...,) x x 2... x n (,,...,)x x 2 x n (,,,...,) x x 2 x 3 x n (,,...,, ) x x 2 x n x n (,,,...,)x x 2 x 3 x n (,,,,...,)x x 2 x 3 x 4 x n (,,...,,, ) x x 2 x n 2 x n x n (,,...,)x x 2 x n = a ( x )( x 2 ) ( x n ) a x ( x 2 ) ( x n ) a 2 ( x )x 2 ( x 3 ) ( x n ) a n ( x )( x 2 ) ( x n )x n a 2 x x 2 ( x 3 ) ( x n ) a 3 x ( x 2 )x 3 ( x 4 ) ( x n ) a n,n ( x )( x 2 ) ( x n 2 )x n x n a 2 n x x 2 x n = a (a x a 2 x 2 a n x n ) (a 2 x x 2 a 3 x x 3 a n,n x n x n ) a 2 n x x 2 x n 3.6 = xy = xy g = xy u = xy ū 7
8 5: x y xy = x y u xy ū = g NAN,,.,., NAN, 5. 5: NAN w =, 6. (x, y,, ) = (x xy) (x ȳ) = x xy x ȳ = x( ) xy ȳ = x xy ȳ, w =, 7. (x, y,, ) = =, 8. x y 3 6 6: (x, y,, ) 7: (x, y,, ) 8
9 x w y 8: 6: A B C A B C , 2 NAN.,,. A =, B., A =, B. A B.,., NAN OR., NOT., B = B =. B =, x NAN =. B =, y NAN =., =., NAN,,,., A=,, 2, 6,. NAN,., NAN.,. 9
10 C A B B 9: 3.8 : 3.8 C 4 4 (,B,C,) B C : 3 = C 4 = C 3 = C( C ) =C 5 = 3 = ( C ) = C 8 = B( C ) = B C B (,B,C,) = = C C B C B A=, 6, 8., NAN 2. B 2 2 C 4 4 B C 9 (,B,C,) C :. 2 = BC
11 A C B 3: 2 = B BC 3 = C BC 4 = C = 2 3 (,B,C,) = C = BC BC B C I H Ī K I H K,, = I H (Ī K) I H K = I H Ī K I H K = I H Ī H Ī K I H K I H K = H Ī K I H = H K Ī IH = H K Ī H = Ī K =. 3.2 xȳ xy =, x x = y 2. 2,
12 ( 2 ) = x x = x(xȳ xy) x(xȳ xy) = x( x y)(x ȳ) xy = xy(x ȳ) xy = (x x)y = y, xȳ xy =, x x = y x y =, x y = 2. 2 ( 2 ) = x y = x y(x y) = x xy y = x y, 2 =, x y =,, =., (x, y, ) =(,, ), (,, ), (,, ) x xy =, xy = x 2. x =. x = 2, y =, y =., (x, y, ) =(,, ). 2
a x x x x 1 x 2 Ý; x. x = x 1 + x 2 + Ý + x = 10 1; 1; 3; 3; 4; 5; 8; 8; 8; 9 1 + 1 + 3 + 3 + 4 + 5 + 8 + 8 + 8 + 9 10 = 50 10 = 5 . 1 1 Ý Ý # 2 2 Ý Ý & 7 7; 9; 15; 21; 33; 44; 56 21 8 7; 9; 15; 20; 22;
f (x) f (x) f (x) f (x) f (x) 2 f (x) f (x) f (x) f (x) 2 n f (x) n f (n) (x) dn f f (x) dx n dn dx n D n f (x) n C n C f (x) x = a 1 f (x) x = a x >
5.1 1. x = a f (x) a x h f (a + h) f (a) h (5.1) h 0 f (x) x = a f +(a) f (a + h) f (a) = lim h +0 h (5.2) x h h 0 f (a) f (a + h) f (a) f (a h) f (a) = lim = lim h 0 h h 0 h (5.3) f (x) x = a f (a) =
a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p
a a a a y y ax q y ax q q y ax y ax a a a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p y a xp q y a x p q p p x p p q p q y a x xy xy a a a y a x
140 120 100 80 60 40 20 0 115 107 102 99 95 97 95 97 98 100 64 72 37 60 50 53 50 36 32 18 H18 H19 H20 H21 H22 H23 H24 H25 H26 H27 1 100 () 80 60 40 20 0 1 19 16 10 11 6 8 9 5 10 35 76 83 73 68 46 44 H11
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
5 5. 2 D xy D (x, y z = f(x, y f D (2 (x, y, z f R 2 5.. z = x 2 y 2 {(x, y; x 2 +y 2 } x 2 +y 2 +z 2 = z 5.2. (x, y R 2 z = x 2 y + 3 (2,,, (, 3,, 3 (,, 5.3 (. (3 ( (a, b, c A : (x, y, z P : (x, y, x
.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(
06 5.. ( y = x x y 5 y 5 = (x y = x + ( y = x + y = x y.. ( Y = C + I = 50 + 0.5Y + 50 r r = 00 0.5Y ( L = M Y r = 00 r = 0.5Y 50 (3 00 0.5Y = 0.5Y 50 Y = 50, r = 5 .3. (x, x = (, u = = 4 (, x x = 4 x,
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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 +
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)
2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................
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0 (18) /12/13 (19) n Z (n Z ) 5 30 (5 30 ) (mod 5) (20) ( ) (12, 8) = 4
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7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
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
20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + 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 = 0 444 ( a, b, c, d
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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 (
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5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h 0 g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)
5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h 0 f(a + h, b) f(a, b) h............................................................... ( ) f(x, y) (a, b) x A (a, b) x
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š ( ) 300,000 180,000 100,000 120,000 60,000 120,000 240,000 120,000 170,000 240,000 100,000 99,000 120,000 72,000 100,000 450,000 72,000 60,000 100,000 100,000 60,000 60,000 100,000 200,000 60,000 124,000
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A 2563 15 4 21 1 3 1.1................................................ 3 1.2............................................. 3 2 3 2.1......................................... 3 2.2............................................
> > <., 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 >
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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
5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................
5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h f(a + h, b) f(a, b) h........................................................... ( ) f(x, y) (a, b) x A (a, b) x (a, b)
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I n n A AX = I, YA = I () n XY A () X = IX = (YA)X = Y(AX) = YI = Y X Y () XY A A AB AB BA (AB)(B A ) = A(BB )A = AA = I (BA)(A B ) = B(AA )B = BB = I (AB) = B A (BA) = A B A B A = B = 5 5 A B AB BA A
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(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
[ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)
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 =
1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i
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ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................
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ii-03.dvi
2005 II 3 I 18, 19 1. A, B AB BA 0 1 0 0 0 0 (1) A = 0 0 1,B= 1 0 0 0 0 0 0 1 0 (2) A = 3 1 1 2 6 4 1 2 5,B= 12 11 12 22 46 46 12 23 34 5 25 2. 3 A AB = BA 3 B 2 0 1 A = 0 3 0 1 0 2 3. 2 A (1) A 2 = O,
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EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
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EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
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橡hashik-f.PDF
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05[ ]戸田(責)村.indd
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301-A2.pdf
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A_chapter5.dvi
5. f,g,h f d,g d,h d. f f = y f d = f(, ȳ) = ȳ = y f f d, f. g g = g d = = g = g d, g. h h = yz y ȳz h d =( y z)( y)( ȳ z) h = h d, h. 5.2 f d ((f d ) d =(f(, 2,..., n )) d = f(, 2,..., n )=f. 5.3 f f