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取扱説明書[N-02B]

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Evolutes and involutes of fronts Masatomo Takahashi Muroran Institute of Technology

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取扱説明書　P703i　日本語

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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

2 1 F M m r G F = GMm r 2 (1.1) (1.1) (r = r ) F = GMmr r 3 (1.2) a F m F = kma k 1 F = ma (1.3) (1.2) (1.3) ma = GMmr r 3 (1.4)

1 1 1.1 2 1 F M m r G F = GMm r 2 (1.1) (1.1) (r = r ) F = GMmr r 3 (1.2) a F m F = kma k 1 F = ma (1.3) (1.2) (1.3) ma = GMmr r 3 (1.4) 1.1 3 M m r a a = d2 r dt 2 (1.4) r d 2 r dt 2 = GM r 3 r (1.5)

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TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7

1 1 x y = y(x) y, y,..., y (n) : n y F (x, y, y,..., y (n) ) = 0 n F (x, y, y ) = 0 1 y(x) y y = G(x, y) y, y y + p(x)y = q(x) 1 p(x) q(

1 1 y = y() y, y,..., y (n) : n y F (, y, y,..., y (n) ) = 0 n F (, y, y ) = 0 1 y() 1.1 1 y y = G(, y) 1.1.1 1 y, y y + p()y = q() 1 p() q() (q() = 0) y + p()y = 0 y y + py = 0 y y = p (log y) = p log

But nothing s unconditional, The Bravery R R >0 = (0, ) ( ) R >0 = (0, ) f, g R >0 f (0, R), R >

2 2 http://www.ozawa.phys.waseda.ac.jp/inde2.html But nothing s unconditional, The Bravery > (, ( > (, f, g > f (,, > sup f( ( M f(g( (i > g [, lim g( (ii g > (, ( g ( < ( > f(g( (i g < < f(g( g(

() 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 >

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2

2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6

version 1.8 12 4 Copyright c 2000 1 1 2 2 2.1........................................... 2 2.2......................................... 2 2.3........................................ 2 2.4......................................

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

[ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

< 1 > (1) f 0 (a) =6a ; g 0 (a) =6a 2 (2) y = f(x) x = 1 f( 1) = 3 ( 1) 2 =3 ; f 0 ( 1) = 6 ( 1) = 6 ; ( 1; 3) 6 x =1 f(1) = 3 ; f 0 (1) = 6 ; (1; 3)

< 1 > (1) f 0 (a) =6a ; g 0 (a) =6a 2 (2) y = f(x) x = 1 f( 1) = 3 ( 1) 2 =3 ; f 0 ( 1) = 6 ( 1) = 6 ; ( 1; 3) 6 x =1 f(1) = 3 ; f 0 (1) = 6 ; (1; 3) 6 y = g(x) x = 1 g( 1) = 2 ( 1) 3 = 2 ; g 0 ( 1) =

高校生の就職への数学II

II O Tped b L A TEX ε . II. 3. 4. 5. http://www.ocn.ne.jp/ oboetene/plan/ 7 9 i .......................................................................................... 3..3...............................