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

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

2 2 V 5Hz.5V.5V V 5Hz 5 t V f(t) = A sin(2π 5t) E = IR, W = EI I ( ) R ( ) W ( ) V A =KW 2π Hz 2π f(t) = A sin t f(t) f(t) 2 f(t) 2 dt = A 2 sin 2 t dt = A 2 π 2π 2π A = 2 V 2V 6V V (t) = NΦ (t) Φ N N N 2 A sin ωt Φ(t) = A N cos ωt V (t) = A N2 N sin(ωt)

3 W J ) J=4.2cal Kcal Cal (MKS ) W = 864 J = 257 Kcal 5W V I = 5A 5 = 2 3 2V 2 = 2 3 I I = 3A 6W 4

4 Hz 939 Hz 2π sin 44 2πt cos 44 2πt sin cos ( π ) cos x = sin 2 x a cos x + b sin x = a 2 + b 2 sin(x + α) sin ωt ω/2πhz sin 2ωt 2.3 sin 3ωt sin ωt sin 2ωt 3 2.:

5 : 2.3: 5 sin 3ωt 2 sin ωt sin ω t sin ωt + sin ω t = 2 sin ω + ω 2 t cos ω ω t 2 ω ω Hz Hz hz 88Hz 32Hz 5 (dominant) : 3

6 6 2 2.: ( ) 9/8 8/ /372 3/2 27/6 243/ # # # # 2 # 3 44Hz Hz = 528Hz 5 ( ) 2 3 = = ( : : = : 5 4 : 3 = 4: 5: 6 2 3: 4: 5 3 4: 5: 6

7 : ( ) 9/8 5/4 4/3 3/2 5/3 5/ log log 2 log 4 2.5: C : 5: 6 : 2: 5 (subdominant) 5: 6 3 : 2: Mathematica 2.3: ( ) 2 2/2 2 4/2 2 5/2 2 7/2 2 9/2 2 /2 2 2/

8 : : 9/8 6/5 4/3 3/2 8/5 9/ : 2: 3: : 5 5: x x 2 f(b) f(a) b a = f (c) c a b f(x) = f(a) + f (a)(x a) + f (a) 2 (x a) 2 + f (a) (x a) 3 + 3! :

9 : 3 2.7: 3 2.8: 3 2.9: 3

10 : f(x) f(x) = N n= n= f (n) (a) (x a) n n! f (n) (a) (x a) n n! (sin x) = cos x, f (N) (x) x N N! (cos x) = sin x (sin x) = cos x, (sin x) = sin x, (sin x) = cos x, (cos x) (4) = sin x cos x = x2 2 + x4 4! x6 6! x8 8! + sin x = x x3 3! + x5 5! x7 7! + n! / 2π (2π) N N! < N N = 22 x 2 x 4 x 2 2. x 22 cos x 2. 2

11 : cos 44 2πx x = 44 2π N = ! e x = + x + x2 2 + x3 3! + = x = e = ! + e e ix = cos x + i sin x cos 2θ+i sin 2θ = e i2θ = (e iθ ) 2 = (cos θ+i sin θ) 2 = cos 2 θ sin 2 θ+2i sin θ cos θ n= x n n! 4. cos(α + β) + i sin(α + β) = e i(α+β) = e iα e iβ = (cos α + i sin α)(cos β + i sin β)

12 2 2 tan arctan y = arctan x x = tan y = dy cos 2 y dx (arctan x) = + x 2 arctan x arctan x = x x3 3 + x5 5 x = π 4 = π tan( π 4 4α) = 239 (tan 5 = α) π 4 = 4 arctan 5 arctan 239 π π. arctan 5 arctan 239 π 3.4 = =, C[, ] [, ] f = max x { f(x) } f g C[, ] d X

13 d(x, y) d(x, y) = x = y 2. d(x, y) d(x, z) + d(z, x) ( ) 6 C[, ]. f g f g = f = g f g = max f(x) g(x) max { f h + h g } x x max f g + max h g = f h + h g x x 7 f(x) = x 2, g(x) = x 3 f g. h(x) = x 2 x 3 f g = 4 27 (Weierstrass) C[, ] P [, ]. X x i x x S n = n Xi x i= f n ( k p n (x) = E[f(S n /n)] = nc k x k ( x) n k f n) k= (Bernstein)

14 4 2 f ε > δ > s.t. x x < δ f(x) f(x ) < ε f(x) p n (x) = [f(x) E f [ E f(x) f = ( Sn ) ] n ) ] ( Sn n {ω : S n (ω)/n x δ} + max 2 f P {ω : S n (ω)/n x <δ} { ω Ω: x( x) max 2 f nδ 2 max f 2nδ 2 + ε ( f(x) f Sn ) dp n ( f(x) f Sn ) dp n } S n (ω) x n δ + ε E(Xi x) = x, V (Xx i ) = x( x) sup norm + ε f p n < max f 2nδ 2 + ε ε 2.3 (768 83) ( )

15 : : [, 2π], cos x, cos 2x,... sin x, sin 2x,... f(x) = a 2 + a n cos nx + b n sin nx n= a = π a n = π b n = π f(x) dx n= f(x) cos nx dx f(x) sin nx dx

16 : : 2 [, 2π] L [, 2π] = {f : L 2 [, 2π] = {f : f(x) dx < } f(x) 2 dx < } L [, 2π] f = f(x) dx, L 2 [, 2π] f 2 = f(x) 2 dx L 2 [, 2π] (f, g) = f(x) g(x) dx, cos x, cos 2x,... sin x, sin 2x,... (sin x, cos x) = sin x cos x dx =

17 , cos x, cos 2x,... sin x, sin 2x,.... 2π, π cos x, π cos 2x,... sin x, sin 2x,... π π

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

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 ),