pdf (it, 2.898,97 KB, 25/01/13)

More documents

Recommendations

Info

$(Microsoft PowerPoint - 03_Gruppi_Alcani [modalit\340 compatibilit ...$

P Q A Q(x, y) = x P (x, y) = 0 +∞ A = x dy = F1(t)F ′ +∞ at 2(t) dt = 1 + t3 · at(2 − t3 ) (1 + t3 +∞ t dt = a2 ) 2 2 (2 − t3 ) (1 + t3 dt ) 3 = a2 3 γ 0 0 +∞ 2 − t 0 3 (1 + t3 ) 3 · 3t2 dt = a2 +∞ 3 0 A = a 2 /6 2 − s a2 ds = (1 + s) 3 3 +∞ 1 0 3 − u a2 du = u3 6 . a > 0 ρ 2 (θ) = 2a 2 cos 2θ. θ [−π/2, 3/2π] 2π cos 2θ ≥ 0 θ ∈ [−π/4, π/4]∪[3/4π, 5/4π] =: D ρ(−π/4) = ρ(π/4) = ρ(3/4π) = ρ(5/4π) = 0 γ C A = dx dy. (P (x, y) dx + Q(x, y) dy) = γ C C ∂Q ∂x ∂P − dxdy, ∂y P : R 2 → R Q : R 2 → R C P Q A Q(x, y) = x P (x, y) = 0 x(θ) = ρ(θ) cos θ y(θ) = ρ(θ) sin θ A = ρ(θ) cos(θ) · ρ D ′ (θ) sin θ + ρ(θ) cos θ dθ = ρ(θ) cos(θ) · ρ D ′ (θ) sin θ + ρ(θ) cos θ dθ = 1 ρ(θ) · ρ 2 D ′ (θ) sin 2θ dθ + 2a 2 cos 2θ cos D 2 θ dθ = 1 d 4 D dθ [ρ2 (θ)] sin 2θ dθ + a 2 cos 2θ · (cos 2θ + 1) dθ D = −a 2 sin 2 2θ dθ + a 2 cos 2 2θ dθ + a 2 cos 2θ dθ = −a 2 + −a 2 D π/4 D sin D −π/4 2 2θ dθ + a 2 π/4 cos −π/4 2 2θ dθ + a 2 π/4 −π/4 5/4π sin 3/4π 2 2θ dθ + a 2 5/4π cos 3/4π 2 2θ dθ + a 2 5/4π 3/4π cos 2θ dθ+ cos 2θ dθ π [3/4π, 5/4π] [−π/4, π/4] A = 2 −a 2 = 2a 2 π/4 −π/4 π/4 sin −π/4 2 2θ dθ + a 2 π/4 cos −π/4 2 2θ dθ + a 2 π/4 −π/4 cos 2θ dθ = 2a 2 , cos 2θ dθ .
cos(π − α) = − cos(α) π/4 −π/4 sin 2 2θ dθ = 2 = 2 π/4 0 π/4 2a 2 0 sin 2 2θ dθ = 2 π/4 cos 2 (π − 2θ) dθ = 2 0 cos 2 (π − 2θ) dθ π/4 0 cos 2 (2θ) dθ = π/4 −π/4 cos 2 2θ dθ. a > 0 ρ(θ) = a(1 + cos θ). ρ(0) = ρ(2π) γ C A = dx dy. (P (x, y) dx + Q(x, y) dy) = γ C C ∂Q ∂x ∂P − dxdy, ∂y P : R 2 → R Q : R 2 → R C P Q A Q(x, y) = x P (x, y) = 0 x(θ) = ρ(θ) cos θ y(θ) = ρ(θ) sin θ 2π A = x dy = ρ(θ) cos θ · = a 2 = a 2 = a 2 = a 2 = a2 8 = a2 4 γ 2π 0 2π 0 (1 + cos θ) cos θ · (1 + cos θ) 2 cos 2 θ dθ − a 2 2π ρ ′ (θ) sin θ + ρ(θ) cos θ dθ − sin 2 θ + (1 + cos θ) cos θ dθ sin 2 θ(1 + cos θ) cos θ dθ 0 2π 0 cos 0 2 θ + cos 4 θ + 2 cos 3 θ − (cos θ − cos 3 θ − cos 4 θ + cos 2 θ) dθ 2π 4 eiθ + e−iθ 2 cos 4 θ + 3 cos 3 θ − cos θ dθ = 2a 2 2π 0 2π (e 0 2iθ + e −2iθ + 2) 2 dθ = a2 8 2π 0 (cos 4θ + 4 cos 2θ + 3) dθ = 3πa2 2 , cos 4 θ dθ = 2a 2 2π 0 0 2π (e 0 4iθ + e −4iθ + 4 + 2 + 4e 2iθ + 4e −2iθ ) dθ (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc 3πa 2 /2 2 dθ
Page 3 and 4:
R R n
Page 5:
2 × 2 SO(
Page 9 and 10:
R a
Page 11:
R F G R F G ¯ F ⊇ G
Page 14 and 15:
R n x, y ∈ Rn x = (x1, ...
Page 17 and 18:
(X, τ) D ⊆ X X
Page 19 and 20:
f : D → R D ⊆ Rn γ : [
Page 21:
A =]0, +∞[×]0, +∞[ f : A →
Page 24 and 25:
lim (x,y)→(0,0) (x,y)=(0,0) |xy|
Page 26 and 27:
E E E f −1 ([1, +∞[)
Page 28 and 29:
s ↦→ 1 − e −s s ≥ 0 1
Page 30 and 31:
Fn : [0, +∞[→ R Fn(ρ) = 2n ρ
Page 33 and 34:
I =]a, b[ R {fn}n∈N fn : I
Page 35:
K [0, +∞[ R > 0 B(0, R) ⊇
Page 38 and 39:
an = 0 n = 2k an = 4/(πn2 ) n
Page 40 and 41:
5 1 18 = + 2 4 π2 ∞ n=0 ∞ n=0
Page 43 and 44:
g(x) := x(π−x) x ∈ [0, π]
Page 45 and 46:
X Y T : X → Y T ℓ >
Page 47 and 48:
X K E X a, b ∈ R f : E × [a
Page 49 and 50:
|f(x, y)| ≤ log(1 + 3y
Page 51 and 52:
(x, y) ∈ R 2 xy =
Page 53 and 54:
X, Y D ⊆ X f : D → Y u ∈
Page 55 and 56:
H A 2 × 2 λ 2
Page 57:
(2kπ, π/2+2hπ) (π+2kπ, 3π/2+2
Page 60 and 61:
∂xf(x, y, z) = −2 cos x sin x =
Page 62 and 63:
(0, 0) f : R 2 → R f(x, y) =
Page 65 and 66:
α ∈ R (0, 0) f(x, y) = 2
Page 67:
Cα > 0 α /∈ [−1/2, −1/4]
Page 70 and 71:
x = cos θ y = sin θ θ ∈ [−π
Page 72 and 73:
γ(t) = (t, 1/t) t → ±∞ L(x
Page 74 and 75:
⎧ ⎪⎨ 1 + λ(2x − 2) = 0, 1
Page 76 and 77:
f(x, y) = x 2 + y 2 V = {(x, y)
Page 78 and 79: ⎧⎪ 2x + λ(2x + y) + 2µx = 0
Page 81 and 82: R 2 D ⊆ R 2 f : D → R (x0,
Page 83 and 84: x = 1 y = −1 z = 2 y z
Page 85: ⎛ 1 ⎜ 3 F (m1, m2, p1, p2) =
Page 88 and 89: k = 3√ 4 ξ ζ
Page 90 and 91: x = ρ cos θ y = ρ sin θ ρ 2 (
Page 92 and 93: f(x, y, z) = ez+x2 f + αx + y
Page 94 and 95: ϕ(1) = 0 ϕ ′ (1) = − ∂xf(1
Page 96 and 97: y 3 − xy 2 + x 2 y = x − x 3
Page 98 and 99: X = {(ρ, θ) ∈ R 2 : ρ > 0, 0 <
Page 100 and 101: arcsin sin θ = θ θ ∈] − π
Page 102 and 103: I R r : I → Rd γ µ : r
Page 104 and 105: γ lunghezza(γ) = |r ′ (θ)|
Page 106 and 107: p = 2 |(x, y)| −p dx dy = R 2 \B
Page 108 and 109: ρ 3 cos θ = aρ 2 (cos 2 θ − s
Page 111 and 112: Γ := {(x, y) ∈ R 2 : (x 2 + y 2
Page 113 and 114: x Γ Q2 Q3 x Γ \
Page 115 and 116: (x 2 + y 2 )(y 2 + x(x + 1)) = 4xy
Page 117 and 118: 4 ±1, ±2, ±4 ±1, ±2 4
Page 119 and 120: −2 + 8t − 4t 2 t = 1/2(2
Page 121 and 122: a ∈ R R 2 (x 2 + y 2 ) 3 = 4
Page 123: (x 2 + y 2 ) 3 = 4x 2 y 2
Page 127: a > 0 x = at at2 , y = . 1
Page 132 and 133: I := F · ˆn dσ ˆn Σ =
Page 134 and 135: S ψ(x, y) = (ψ1, ψ2, ψ3) = (
Page 136 and 137: C = {(x, y, z) : (x, y) ∈ D, λ <
Page 138 and 139: ˆn = ∇G = ((∇G)1, (∇G)2, (
Page 140 and 141: 2π 0 cos θ sin θ dθ = 1 2 2π
Page 142 and 143: L − F · ˆn dσ = − L− √
Page 145 and 146: K ⊆ R n χK : R n → {0, 1}
Page 147 and 148: f [1, +∞[ [0, 1] [0
Page 149 and 150: f α k = 1 x α + k α , sα n = n
Page 151 and 152: D R X n 1 1 X C ℓ
Page 153 and 154: γ2(1/2) = (1/8, 3/4) γ2(1) = (0,
Page 155 and 156: C = −B ∂yu(x, y) = C/x 1 + y2 y
Page 157 and 158: dy N(x, y) = − dx M(x, y) N M
Page 159 and 160: 2xy dx + (x 2 + 1) dy = 0 (x 2 + y
Page 161 and 162: x − c = arcsin(2y − 1) 0 < y
Page 163: h(x, y) = 1/(|x| √ x2 − 1)
Page 166 and 167: ˙x = e t−x /x x(α) = 1 α ∈ R
Page 168 and 169: ˙x = x 2 /(1 − tx) x(0) = α α
Page 170 and 171: y ′′′ − 6y ′′ + 11y ′
Page 172 and 173: c ′ 1 (x) cos x + c′ 2 (x) sin
Page 175 and 176: y ′ + y 1 x = tan x sin x y ′
Page 177 and 178: λ 2 − 4λ − 5 = 0, A
Page 179 and 180:
F (x, y, ˙y) = 0, F : A → R A
Page 181 and 182:
F (x, y, p) = 0 c = 0 dy = p dx
Page 183:
y = xy ′ + f(y ′ ) F (x, y, p
Page 186 and 187:
y → 0 −∞
Page 188 and 189:
x > 0 x y = ± 1 + x x < 0
Page 191 and 192:
[0, π] utt + 2ut − uxx = 0,
Page 193 and 194:
e |uk(x, t)| = C −t sin( 4k(1
Page 195:
∞ n=1 bne −x sin nx = x(
Page 198 and 199:
T ˙ Tn(t) = −5n 2 Tn(t) Tn(
Page 200 and 201:
⎧ −utt + 3uxx = 0 ]0, π[×]0,
Page 202 and 203:
∆ = 0 λ = −1 µ1 = µ2 = −
Page 204 and 205:
x = cos θ y = sin θ F F (co
Page 206 and 207:
I := arctan y dx − xy dy γ γ
Page 208 and 209:
f(ρ) f ′ (ρ) = 4ρ3 + 36ρ 8
Page 210 and 211:
Jac ϕ(θ, y) = ⎛ ⎜ ⎝ − y
Page 212 and 213:
z = (x, y) ˙z = Az + B(t)
Page 214 and 215:
Q0 Q2 Q1 Q1
Page 216 and 217:
˙x = t − x 2 x(0) = a a ∈ R
Page 219 and 220:
2π xt sin t F (x) = e dt x ∈ R
Page 221 and 222:
xz 3 dx dy dz, T T y
Page 223 and 224:
α > 0 lim (x,y)→(0,0) (x,y)=(0,0
Page 225 and 226:
F (0, 1) = 0 ∂yF (x, y) = 3y 2
Page 227 and 228:
(u + v) D 2 + (u − v) 2 1 + 2(u2
Page 229 and 230:
α = = 2 3 π. 2π 0
Page 231 and 232:
F D z = 0 (0,
Page 233 and 234:
y ′ = 2xy − x y(0) = 3/2
Page 235 and 236:
Γ f(x, y) = 0 f : R 2 → R
Page 237 and 238:
∇f(x0, y0) = (0, 0) (x0, y0)
Page 239 and 240:
ϕ : I ×J → R 3 I, J R
Page 241 and 242:
ψ(a, t) = ψ(b, t) t ∈]c, d[
Page 243 and 244:
[
Page 245 and 246:
Y K Ω R × Ω I R f :
Page 247 and 248:
1 ω(x, y) = M(x, y) dx + N(x, y)
Page 249 and 250:
M(x, y) dx + N(x, y) dy = 0 1 M, N
Page 251:
x, y z dy dz
Page 254 and 255:
f(x) = N(x) Ak1 = + D(x) x − xk
Page 256 and 257:
Φ y ′ = A(t) y ′ = A(t)
Page 258 and 259:
det P = 4 √ 7 = 0 P −1 AP
Page 260 and 261:
y ′′ (t) + py ′ (t) + qy(t) =
Page 262 and 263:
y(0) = c1 + d1 = 1 ˙y(t) = (−c1
Page 264 and 265:
a ′ x + b ′ y + c ′ = 0
Page 266 and 267:
η2 g g(η) > 0 y0 < η <
Page 269 and 270:
2 × 2 F ∈ R[x] n
Page 271:
2 × 2 t ↦→ x(
Page 274 and 275:
∆ < 0 α = −d 2c ω = √ |
Page 276 and 277:
a = 0 b = 0 c = 0 ⎧ ⎪⎨ b
Page 279 and 280:
SO(3) U(3) := {O ∈
Page 281:
SO(3) Aξ = ω × ξ ξ
Page 284 and 285:
x 2 + y 2 = 1 x 2 − y 2 = 1
Page 286 and 287:
1 arcsin(x) + x − x2 dx = √ 1
Page 288 and 289:
z 1 + cos z cos = ± 2 2 z 1
show all

pdf (it, 2.898,97 KB, 25/01/13)

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?