fx-JP500
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- とき わくや
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1 SA1409-A JA fx-jp500 RJA V01
2
3 2
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5 n /
6 (RESET) ( ) () (OFF) : 10 (SETUP)() : 5
7 (1) (2) (1) sin 1 D s (2) n (1) (2) (1) (2) (3) (3) / / FIX / SCI M (D)(R) (G) (Fix) FIX(Sci) SCI 6
8 / / (SETUP) (1) (2) (1) (2)
9 : : n / 3. : : * 1 * 2 * 2 (SETUP) (/) : ( ) (/) () ( /) *1 *2 1 S-V.P.A.M. 8
10 / / / / / n/ / 1. (SETUP) / ; /; ; / 9
11 (D) ; (R); (G) (Fix): 0 9 : 100 7( )* ( (Fix) 3) (Sci): 0 9 : 1 7( )* ((Sci) 5) (Norm): (Norm) 1 : 10 2 > x, x (Norm) 2: 10 9 > x, x : ( )* ((Norm) 1) ((Norm) 2) * ( ) (ab/c); (d/c) (a+bi) ; (r) / : i ; (Freq) / ; / f (x); f (x),g (x) f (x) 2 f (x) g (x) ; 10
12 ; : (,) (;) 3; 3 English; ( ) (RESET) () () 4 sin 30 ( ) = * 2 * 1 *1 sin *2 ( ) * * 3 11
13 - : 6 2(1 + 2) 6 (2(1 + 2)) 1 (2 + 3)sin(30) 1 ((2 + 3)sin(30)) - : (2 )2 2'2 2 (2'2 ) 1 2 sin( log( 3 (x 2 x 3 x 1 x! r g %t) ( ) ( ) 4 5 (( )) n (d h b o) 6 (cm in) ( 1 2 ) 7 8 (npr) (ncr) ( ) 9 ( ) ( ) ( R) 10 (+) ( ) 11 and ( ) 12 or xor xnor ( ) : x 2 ( ) 22 2 ( / ) 12
14 : ( ) ( ) Σ / / 2 / (/ ) (UNDO) (UNDO) 13
15 ( / ) : (INS) (INS) 7 6 ( / ) (INS) / / 6 = 1 6 π = ( ) 1 ( ) 6 6 π ( 2 + 2) 3 = = (/) / = 1 5 = 0.2 ()
16 10 ( ) / ( ) 2 3( ) () ( ) (%) % = (%) (75%) (%) % (2625) (%)
17 60 60{ } { } { }0 0 : = (6010) (1060) (:) : (:) : / / (:) ENGENG ENG ENG ( ) ( ) R 5 2 5( R) 2 16
18 / / (FACT) (FACT) : 10 1,018, ( 4 ) ( ) 0 ( 4 ) / / 17
19 (SETUP) () () 1 ( 4 ) ( 4 ) 312 : (Norm/Fix/Sci) (Norm/Fix/Sci) 1 7 = = (Norm 1) 1 7 : Norm 1: :
20 n = = (1) 4 : / = = 5 () 7 5 (Ans)/ (PreAns) Ans Ans PreAns Ans PreAns : PreAns PreAns Ans: ()7 19
21 = = 210 () 789 PreAns: T k+2 = T k+1 + T k ()T 1 T 5 T 1 = 1 T 2 = 1 T 1 = 1 1 (Ans = T 1 = 1) T 2 = 1 1 (Ans = T 2 = 1, PreAns = T 1 = 1) T 3 = T 2 + T 1 = (PreAns) (Ans = T 3 = 2, PreAns = T 2 = 1) T 4 = T 3 + T 2 = T 5 = T 4 + T 3 = (Ans = T 4 = 3, PreAns = T 3 = 2) (A B C D E F M x y) 3 + 5A 3 5(A) 8 A10 () (A) 10 * 1 80 A () (RECALL)* 2 20 (A) 8 A 0 (A) 0 *1 x (x) *2 (RECALL) (Norm) 1
22 (M) MM M 0 M M 0 (M) M () M () 10 5(M ) 15 M () (RECALL) (M) 35 : M M (RESET) ( ) () : : : = e: e = sin, cos, tan, sin 1, cos 1, tan 1 : sin 30 = 1 2 ( : (D)) sin = 30 ( : (D)) (sin 1 )
23 sinh, cosh, tanh, sinh 1, cosh 1, tanh 1 : ( )* 1 sinh 1 = ( ) (sinh) *1, r, g : r g ()* 2 /2 = 90 (: (D)) ( ) 2 () ( r ) 90 *2, : e 5 2 = ( ) ( ) () ( ) log: log (a, b) a 10 log = log 1000 = log 2 16 = 4 2(,)16 4 / /( ) log 2 16 = 4 ( ) ln: e ln 90 (= loge 90) = x 2, x 3, x,,,, x 1 : (1 1) 2 2 = (5 2 ) 3 = (x 3 ) = 2 ( ) ( ) () 5( )
24 '2 3 = 3'2 = ( ) 23 3'2 () : - Gauss-Kronrod / b a f (x)dx / ( f (x), a, b, tol) tol e ln(x)dx ( ) (x)1 (e) 1 () (x) (,) 1(,)(e) 1 f(x) (R) tol tol : / d dx ( f(x)) x=a / d ( f(x), a, tol) dx tol y = sin(x) x = /2 (: (R)) ( ) (x) (1) ( ) (1) ( ) 2 0 () (1) (,)( ) 2 0 f (x) (R) tol tol
25 0 b : f(x) Σ ( f(x)) = f(a) f(a 1) f(a 2)... x a f(b) / b Σ ( f(x)) x a / Σ( f(x), a, b) a b < a b < Σ (x 1) = 20 x 1 ( ) ( )(x) () ( )(x) 1 (,) 1(,) 5 20 Pol, Rec: Pol Rec r x y x y 180 < 180 Pol(x, y) = (r, ) Rec(r, ) = (x, y) ( 2, 2 ) (: (D)) ( ) (Pol) 2 (,) 2 r=2, =45 ( 2, 45 ) (: (D)) ( ) (Rec) 2 (,) 45 x=1, y=1 x!: (5 + 3)! = (x!)
26 Abs: = 10 ( ) (Abs) () (Abs) Ran#: / (Ran#) 459 RanInt#: 16 (RanInt) 1(,) 6 2 npr, ncr: (npr)(ncr) 10 4 : 10(nPr) : 10(nCr) Rnd: (Fix) = Rnd (Fix) 3Rnd(10 3) = (Norm) 1 (Norm) Rnd(10 3) 3(Fix) 3 (/) (SETUP) () ( (Fix)) (Rnd) GCD, LCM: (GCD)(LCM) 28 35: (GCD) 28(,) : (LCM) 9(,)
27 (a bi)(r) (1 i) 4 (1 i) 2 = 4 2i ( : a bi)* 1(i)4 1(i) 4 2i 2 45 = '2 '2 i (: (D): a bi) 2 ( ) 45 '2 '2 i '2 '2 i = 2 45 (: (D): r) 2 2(i) 2 45 * (a + bi) n n (n: ) 180 < 180 / /a bi r i (Conjg) ( : a bi) ( ) 2 3 (i) 2 3i 1 + i (Abs) (Arg) (: (D)) : (Abs) 1(i) '2 : () 1(i) i (Rep) (Imp) : () 2 3 (i) 2 : () 2 3 (i) 3 r a+bi 26
28 '2 '2 i = 2 45, 2 45 = '2 '2 i (: (D)) 2 2(i) ( r ) 2( ) 45 ( a+bi) 2 45 '2 '2 i : 2x 3y 2Ax 3By C A Bi : x y : x (x y) {} = {1} : y = x 2 x 3 : / 3A + B A = 5 B = 10 3(A) (B) 5 10 : y = x + 5, x = sin(m), x + 3 = B + C, xy + C (xy + C = 0 ) sin log (SOLVE) / 27
29 x 2 b = 0 b = 2x (x)(b)(=) 0 (SOLVE) x (x=1 ): 1 B 2 : 2 (x x ): : (1) (2) (3) () () (1) (2) (3) () ()0 : [=] x 1 y = sinx y = e x y = 'x 28
30 1. 2. : 1 (x) 2 (x, y) 1 : (1) (y = a + bx) 2 (x, y) 2 (y = a + bx + cx 2 ) 2 (x, y) 2 (x, y) e 2 (x, y) ab 2 (x, y) 2 (x, y) (y = a + b ln(x)) (y = a e^(bx)) (y = a b^x) (y = a x^b) (y = a + b/x) : () x 160xFreqx y 2 80x yfreq 3 53 (Freq) / 1 ( ) 2 () 29
31 1: (170, 66), (173, 68), (179, 75) () (y = a + b ln(x)) : 1 2 : 1 : 1 () () () () (1 2) (1 2) 2 () () σxx 2 1 (*) 30
32 : Σx* Σx 2 * Σy Σy 2 Σxy Σx 3 Σx 2 y Σx 4 () : n* / : *, / : σ 2 x*, σ 2 y / : σx*, σy / : s 2 x*, s 2 y / : sx*, sy (// ), : (σx) (sx) σ x = Σ (x ) 2 n Sx = Σ (x ) 2 n 1 : min(x)*, min(y) / : max(x)*, max(y) 1 ( / ), 2 ( / ) 1: Q 1 * / : Med* / 3: Q 3 * (1) ( / ) : a, b / : r / :, () 2 : a, b, c / : 1, 2, () 1 2 : ab y = a b^x Σlny lnb. Σx n. a = exp( n ) Σxlny Σx. Σlny b = exp( n. Σx 2 ) (Σx) 2 lny lna r = n. Σxlny Σx. Σlny = = ab x {n. Σx 2 (Σx) 2 }{n. Σ(lny) 2 (Σlny) 2 } lnb 2: 1 x = {1, 2, 2, 3, 3, 3, 4, 4, 5} {xn; freqn} = {1;1, 2;2, 3;3, 4;2, 5;1} (SETUP)() () () (1) (// ) ( ) 3: (x, y) = (20, 3150), (110, 7310), (200, 8800), (290, 9310)
33 (SETUP)() ( ) (SETUP) () ( (Fix)) () (y = a + b ln(x)) () (r) () (a) () (b) 2 x y y x 2 x 1 x 2 4: 3x = 160 y () ( ) : 1 () P, Q, R: t P(t ) Q ( t ) R ( t) 0 t 0 t 0 t t: ( ) (σx) x x t = x σx x 5: 1 {xn ; freqn} = {0;1, 1;2, 2;1, 3;2, 4;2, 5;2, 6;3, 7;4, 9;2, 10;1}x = 3 P(t) 32
34 (SETUP)() () () (1) () ( t) () (P() n n n : 10 : (DEC) 16 : (HEX) 2 : (BIN) 8 : (OCT) (BIN) F (HEX) 1 (F) 1 16 (A)(B)(C)(D)(E)(F) n 32 2 : x : x : x : x x : x 7FFFFFFF : x FFFFFFFF 33
35 d (10 ) h (16 ) b (2 ) o (8 ) (DEC) (d) 10(h) 10 (b) 10(o) : (DEC) 16 : (HEX) 2 : (BIN) 8 : (OCT) (DEC) (HEX) B (and, or, xor, xnor, Not, Neg)2( (BIN)) ( and ) (and) (Not( )) (Not) : n10 / / / 2. 34
36 : : ( ) ( ) 3. 2x 2 + x 3 = 02( ) (A, B, C, D, E, F, M, x, y) : : ( ) ( ) 0 / x + 2y = 3 2x + 3y = 4 ( ) (x=) 1 (y=) 2 35
37 x 2 + 2x 2 = 0 ( ) (x 1 =) 1 '3 (x 2 =) 1 '3 (y = x 2 + 2x 2 x *) (x=) 1 (y = x 2 + 2x 2 y *) (y=) 3 * y = ax 2 bx c x y 2 12 f(x) = x g(x) = x x 1 0.5: (SETUP)() ( f(x),g(x)) 3. x x (x)1 2 (x) x xf(x) g(x) x 1 x
38 x f (x) g (x) 4g (x) 5 f (x) f (x)45f (x),g (x)30 x : / 47 n : c 0 ( ) 1. () 2. () 3. (c 0 ) CODATA (2010) : c 0 = 1 ε0μ0 1()(ε 0 ) ()( 0 ) 37
39 (n ) : 5 (cm)(in)() 1. 5() 2. () 3. m (m) 4. (cm in) 23 NIST Special Publication 811 (2008)26 cal15 C : 38
40 0 2 () 1 1 () tol 39
41 (RESET) () () : 1. (OFF) (RESET) ( ) () 40
42 ± ± ±1 ±1 sinx cosx 0 x x < x < tanx sinx x = (2n 1) 90 sinx x = (2n 1) /2 sinx x = (2n 1) 100 sin 1 x, cos 1 x 0 x 1 tan 1 x 0 x sinhx, coshx 0 x sinh 1 x 0 x cosh 1 x 1 x tanhx 0 x tanh 1 x 0 x logx, lnx 0 x x x e x x 'x 0 x x 2 x x 1 x ; x 0 3 'x x x! 0 x 69 (x ) npr 0 n , 0 r n (n, r ) 1 {n!/(n r)!}
43 ncr Pol(x, y) 0 n , 0 r n (n, r ) 1 n!/r! n!/(n r)! x, y x 2 + y Rec(r, ) x y x y a b /c 0 r : sinx a, b, c ; 0 b, c 2 ±1 x x x 0: ylogx 100 x = 0: y 0 x 0: y = n, m (m, n ) 2n ylog x 100 y 0: x 0, /x logy 100 y = 0: x 0 2n 1 y 0: x = 2n 1, m (m 0; m, n ) /x log y RanInt#(a, b) a b; a, b ; b a x y x y 3 x! npr ncr 1 / x < 10 6 : : : : : LR C 40 C mm 90 g 42
44 / / 1 : : 2 : : FIX SCI (SETUP) () ((Norm)) () (RESET) () () ) ) 43
45 : (sin 30) + 15 (: (D)) S-V.P.A.M. : : () sin
46 () () : h : : c 0 : ε0 : µ0 : Z 0 : G : l P : t P ( ) : µn : µb : e : φ0 : G 0 : K J ( ) : R K : m p : m n : m e : m μ : a 0 : α : r e : λc : γp : λcp : λcn : R : µp : µe : µn : µμ : m τ () : u : F : N A : k : V m : R : c 1 : c 2 : σ ( ) : g : atm : R K-90 : K J-90 ( ) : t h c 0 ε 0 µ 0 Z 0 G l P t P µ N µ B e φ 0 G 0 K J R K m p m n m e m µ µ a 0 α r e λ C γ p λ Cp λ Cn R µ p µ e µ n µ µ µ m τ u F N A k V m R c 1 c 2 σ- g atm R K-90 K J-90 t 45
47 () () ( ) (m) : cm in : m ft : m yd : km mile : m n mile : km pc : m Å : m fm : m ch : m ua : m l.y. : m mil : m fath : m : cm : mm : m : m : km : km : m : mm : mm (in) : in cm : in ft : in yd : in ch : in mil : in fath (ft) : ft m : ft in : ft yd : ft mile : ft n mile : ft ch : ft fath (yd) : yd m : yd in : yd ft : yd mile : yd ch : yd fath () ( ) (mile) : mile km : mile ft : mile yd : mile ch (ch) : ch m : ch in : ch ft : ch yd : ch mile (fath) : fath m : fath in : fath ft : fath yd (n mile ) : n mile m : n mile ft () ( ) (mil) : mil m : mil in ( ) : m : ( ) : m ( ) : m 46
48 () ( ) ( ) ( ) () ( ) () ( ) : km : cm km : : m ( ) : pc km : Å m : fm m : ua m : l.y. m : mm : mm : mm () ( ) (acre) : acre m 2 : acre mile 2 (m 2 ) : m 2 acre : m 2 b : m 2 a : m 2 ha : cm 2 ft 2 : cm 2 in 2 : km 2 mile 2 : m 2 : m 2 : m 2 : m 2 : m 2 : m 2 : m 2 (a) : a m 2 : a ha (ha) : ha m 2 : ha a () ( ) (mile 2 ) : mile 2 km 2 : mile 2 acre ( ) : m 2 ( ) : m 2 ( ) : m 2 () ( ) ( ) : m 2 ( ) : b m 2 : ft 2 cm 2 : in 2 cm 2 : m 2 : m 2 () ( ) : m 2 (gal(uk) : gal(uk) L ) : gal(uk) bu (L) : L gal(us) : L gal(uk) : L m 3 : L bu : L bbl : ml fl oz(us) : ml fl oz(uk) : L : L : L : L : L 47
49 (m 3 ) : m 3 L : m 3 ton : m 3 ft 3 : m 3 in 3 : cm 3 (bu) : bu L : bu gal(uk) () ( ) ( ) : L ( ) : cm 3 ( ) ( ) () ( ) : L : L : L ( ) : L ( ) : gal(us) L : bbl L : ton m 3 : fl oz(us) ml : fl oz(uk) ml : ft 3 m 3 : in 3 m 3 ( ) : r rad : rad r () ( ) (oz) : oz g : oz lb : oz ton(long) : oz ton(short) (g) : g oz : kg lb : kg mton : kg ton(long) : kg ton(short) : mg mcarat : kg : g : g : g : g : g (lb) : lb kg : lb oz : lb ton(long) : lb ton(short) (ton(long) ) () ( ) (ton(short) ) ( ) : ton(long) kg : ton(long) oz : ton(long) lb : ton(short) kg : ton(short) oz : ton(short) lb : kg 48
50 ( ) ( ) : g : g () ( ) ( ) : mton kg : mcarat mg : g : g : g () (s) ( ) () (m/s) ( ) ( ) : Gal m/s 2 : m/s 2 Gal : s t-yr : s min : s h : s day : t-yr s : min s : h s : day s : m/s km/h : m/s mile/h : m/s knot : km/h m/s : mile/h m/s : knot m/s ( ) : N m dyn cm : dyn cm N m ( ) (N) ( ) () : N dyn : N lbf : N kgf : dyn N : lbf N : kgf N (Pa) : Pa atm : Pa mmhg : Pa kgf/cm 2 : kpa lbf/in 2 : Pa bar : Pa dyn/cm 2 : Pa lbf/in 2 : Pa cmh 2 O : Pa inhg ( ) : atm Pa : mmhg Pa : kgf/cm 2 Pa : lbf/in 2 kpa : bar Pa : dyn/cm 2 Pa : lbf/in 2 Pa : cmh 2 O Pa : inhg Pa 49
51 ( ) (J) : J kgf m : J cal : J erg : J ev : J Btu : J cal IT : J cal th : J W h ( ) : kgf m J : cal J : erg J : ev J : Btu J : cal IT J : cal th J : W h J ( ) : hp kw : kw hp () : Btu/h W : W Btu/h () : FC : CF () : cal th /(g K) J/(kg K) : J/(kg K) cal th /(g K) () : P Pa s : Pa s P ( ) : St m 2 /s : m 2 /s St () : G T : T G : Oe A/m : A/m Oe : Mx Wb : Wb Mx : γ T : T γ ( ) : sb cd/m 2 : cd/m 2 sb : ph lx : lx ph ( ) : Ci Bq : Bq Ci : rad Gy : Gy rad : rem Sv : Sv rem : R C/kg : C/kg R 50
52 /: : (D) 1 I AB c B AC bbc a sin = b c cos = a c tan = b a sin = b c b = c sincos = a c a = c cos 10m (c) B 60 ( θ ) a A b C b = 10 sin 60 : a = 10 cos 60 : bbac b tan b sin abb c a tana cos 10, 60 : (Rec) 10 (,) 60 y 0 10m 60 x P(x,y) 2 II 2 a b B A 1 tan = b a = tan 1 ( b a ) B θ c 8m (a) 5m (b) C = tan 1 (5 8): (tan 1 ) : ac cos 1 ( a c )bc sin 1 ( b c ) B 51
53 5m r P(8,5) 0 θ 8m 8, 5 r, : (Pol) 8(,) 5 y 60 : (RECALL) (y) 3 CDA X A sin C X = sin (180 C D) A (50m) X C (61 32 ) (49 25 )D C D C D (C) (D) 50 (C) 180 (C) (D) 4 abc S S = s (s a)(s b)(s c) 1 s = (a + b + c) 2 s A (A) S (A) (A) 50 (A) 40(A) 30 c (30m) S a (50m) b (40m) 52
54 5 20W 60N 0.3 P P = W (sin + cos ) θ (20 ) P W (60N) 6 V 0 30m/s50 3h h = V 0 t sin 1 2 gt2 g: 9.8m/s θ (50 ) V0(30m/s) h 53
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8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
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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3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
*3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i i r 3r + 4i 1 i 1 i *4 1 i 9 i 1 1 i i 3 9 +
1 2 IT 1 *1 1 2 3 π i 1i 2i 3i πi i 2 1 *2 2 + 3 + 4i π ei 3 4 4 2 2 *1 *2 x 2 + 1 = x 2 + x + 1 = 2 3 1 2 2 2 2 *3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i 1 2 1 2 2 1 i r 3r + 4i 1
( z = x 3 y + y ( z = cos(x y ( 8 ( s8.7 y = xe x ( 8 ( s83.8 ( ( + xdx ( cos 3 xdx t = sin x ( 8 ( s84 ( 8 ( s85. C : y = x + 4, l : y = x + a,
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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
1 (1) ( i ) 60 (ii) 75 (iii) 15 () ( i ) (ii) 4 (iii) 7 1 ( () r, AOB = θ 0 < θ < ) OAB A OB P ( AB ) < ( AP ) (4) 0 < θ < sin θ < θ < tan θ 0 x, 0 y (1) sin x = sin y (x, y) () cos x cos y (x, y) 1 c
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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p.16 1 sin x, cos x, tan x a x a, a>0, a 1 log a x a III 2 II 2 III III [3, p.36] [6] 2 [3, p.16] sin x sin x lim =1 ( ) [3, p.42] x 0 x ( ) sin x e [3, p.42] III [3, p.42] 3 3.1 5 8 *1 [5, pp.48 49] sin
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1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67
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2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 5 Mon, 2006, 401, SAGA, JAPAN Dept.
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[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s
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1 2006 6 NETES No.CG-050001-V 2007 5 2 1 2 1 19 5 1 2 19 8 2 i 1 1 1.1 1 1.2 2 1.3 2 2 3 2.1 3 2.2 8 3 9 3.1 9 3.2 10 3.3 13 3.3.1 13 3.3.2 14 3.3.3 14 3.3.4 16 3.3.5 17 3.3.6 18 3.3.7 21 3.3.8 22 3.4
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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) = (, )
.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 =,
[ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b
1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2
filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin
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22 I 4-4 ( ) 4, [,b] 4 [,b] R, x =, x n = b, x i < x i+ n + = {x,,x n } [,b], = mx{ x i+ x i } 2 [,b] = {x,,x n }, ξ = {ξ,,ξ n }, x i ξ i x i, [,b] f: S,ξ (f) S,ξ (f) = n i= f(ξ i )(x i x i ) 3 [,b] f:,
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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
θ i ) AB θ ) A = B = sin θ = sin θ A B sin θ) ) < = θ < = Ax Bx = θ = sin θ ) abc θ sin 5θ = sin θ fsin θ) fx) = ax bx c ) cos 5 i sin 5 ) 5 ) αβ α iβ) 5 α 4 β α β β 5 ) a = b = c = ) fx) = 0 x x = x =
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yoshi@image.med.osaka-u.ac.jp http://www.image.med.osaka-u.ac.jp/member/yoshi/ II Excel, Mathematica Mathematica Osaka Electro-Communication University (2007 Apr) 09849-31503-64015-30704-18799-390 http://www.image.med.osaka-u.ac.jp/member/yoshi/
all.dvi
38 5 Cauchy.,,,,., σ.,, 3,,. 5.1 Cauchy (a) (b) (a) (b) 5.1: 5.1. Cauchy 39 F Q Newton F F F Q F Q 5.2: n n ds df n ( 5.1). df n n df(n) df n, t n. t n = df n (5.1) ds 40 5 Cauchy t l n mds df n 5.3: t
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40 4 4.3 I (1) I f (x) C [x 0 x 1 ] f (x) f 1 (x) (3.18) f (x) ; f 1 (x) = 1! f 00 ((x))(x ; x 0 )(x ; x 1 ) (x 0 (x) x 1 ) (4.8) (3.18) x (x) x 0 x 1 Z x1 f (x) dx ; Z x1 f 1 (x) dx = Z x1 = 1 1 Z x1
II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
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II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh