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 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 96 2 2 W J ) J=4.2cal Kcal Cal (MKS ) W 36 24 = 864 J = 257 Kcal 5W V I = 5A 5 = 2 3 2V 2 = 2 3 I I = 3A 6W 4
4 2 2. 44Hz 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 2. 2.2 sin 2ωt 2.3 sin 3ωt sin ωt sin 2ωt 3 2.:
2.. 5 2.2: 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 3 2 5 44Hz 2. 2.2 88Hz 2.3 32hz 88Hz 32Hz 5 (dominant) 3 5 2.4: 3
6 2 2.: ( ) 9/8 8/64 7747/372 3/2 27/6 243/28.25.26563.3552.5.6875.89844 5 # # # # 2 # 3 44Hz Hz. 9 39 2 4.2 44.2 = 528Hz 5 ( ) 2 3 = 29.746 2 7 2 7 29.746 2 7 =.364 3 ( 3 2 3 3 5 4 5 3 : : = : 5 4 : 3 = 4: 5: 6 2 3: 4: 5 3 4: 5: 6
2.. 7 2.2: ( ) 9/8 5/4 4/3 3/2 5/3 5/8 2.25.25.333.5.667.875 2 log log 2 log 4 2.5: 2 2.2 C 3 3 2.5 2 2.3 3 2.4 2 3 3 3 4: 5: 6 : 2: 5 (subdominant) 5: 6 3 : 2: 5 2.5 2.6 Mathematica 2.3: ( ) 2 2/2 2 4/2 2 5/2 2 7/2 2 9/2 2 /2 2 2/2.22.26.335.498.682.888 2
8 2 2.4:.997744.794.3.99887.98.68 2.5: 9/8 6/5 4/3 3/2 8/5 9/5 2 2.6 : 2: 3: 5 2.7 4: 5 5: 6 3 2.8 2.9 3 2.2 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! 528 594 66 74 792 88 99 48 523.25 587.33 659.26 698.46 783.99 88. 987.77 46.5 528.596 594.67 66. 74.795 792.894 88. 99. 57.9 2.6:
2.2. 9 2.6: 3 2.7: 3 2.8: 3 2.9: 3
2.75.5.25 -.25 -.5 -.75-2 3 4 5 6 2.: 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
2.2..5 2 3 4 5 6 -.5-2.: cos 44 2πx x = 44 2π N = 759 759! e x = + x + x2 2 + x3 3! + = x = e = + + 2 + 3! + 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)
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 = 3 + 5 π tan( π 4 4α) = 239 (tan 5 = α) π 4 = 4 arctan 5 arctan 239 π 5 3.4 π. arctan 5 arctan 239 π 3.4 = 5 5 3 3 +.97333 =, 484 239 C[, ] [, ] f = max x { f(x) } f g C[, ] d X
2.2. 3. 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)
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) ( )
2.3. 5.8.6.4.2 2 3 4 5 6 2.2:.5 2 4 6 8 2 -.5-2.3: [, 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 7 2.4 2.5 9
6 2.8.6.4.2 2 4 6 8 2 2.4:.5 -.5 2 4 6 8 2-2.5: 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 =
2.3. 7 8, cos x, cos 2x,... sin x, sin 2x,.... 2π, π cos x, π cos 2x,... sin x, sin 2x,... π π