- 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
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R n x, y ∈ Rn x = (x1, ...
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(X, τ) D ⊆ X X
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f : D → R D ⊆ Rn γ : [
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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]
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X Y T : X → Y T ℓ >
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X K E X a, b ∈ R f : E × [a
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|f(x, y)| ≤ log(1 + 3y
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(x, y) ∈ R 2 xy =
- Page 53 and 54:
X, Y D ⊆ X f : D → Y u ∈
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H A 2 × 2 λ 2
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(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) =
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α ∈ R (0, 0) f(x, y) = 2
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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)
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⎧⎪ 2x + λ(2x + y) + 2µx = 0
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R 2 D ⊆ R 2 f : D → R (x0,
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x = 1 y = −1 z = 2 y z
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⎛ 1 ⎜ 3 F (m1, m2, p1, p2) =
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k = 3√ 4 ξ ζ
- Page 90 and 91:
x = ρ cos θ y = ρ sin θ ρ 2 (
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f(x, y, z) = ez+x2 f + αx + y
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ϕ(1) = 0 ϕ ′ (1) = − ∂xf(1
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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
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x Γ Q2 Q3 x Γ \
- Page 115 and 116:
(x 2 + y 2 )(y 2 + x(x + 1)) = 4xy
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4 ±1, ±2, ±4 ±1, ±2 4
- Page 119 and 120:
−2 + 8t − 4t 2 t = 1/2(2
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a ∈ R R 2 (x 2 + y 2 ) 3 = 4
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(x 2 + y 2 ) 3 = 4x 2 y 2
- Page 127 and 128:
a > 0 x = at at2 , y = . 1
- Page 129:
cos(π − α) = − cos(α) π/4
- Page 132 and 133:
I := F · ˆn dσ ˆn Σ =
- Page 134 and 135:
S ψ(x, y) = (ψ1, ψ2, ψ3) = (
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C = {(x, y, z) : (x, y) ∈ D, λ <
- Page 138 and 139:
ˆn = ∇G = ((∇G)1, (∇G)2, (
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2π 0 cos θ sin θ dθ = 1 2 2π
- Page 142 and 143:
L − F · ˆn dσ = − L− √
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K ⊆ R n χK : R n → {0, 1}
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f [1, +∞[ [0, 1] [0
- Page 149 and 150:
f α k = 1 x α + k α , sα n = n
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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 ′
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λ 2 − 4λ − 5 = 0, A
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F (x, y, ˙y) = 0, F : A → R A
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F (x, y, p) = 0 c = 0 dy = p dx
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y = xy ′ + f(y ′ ) F (x, y, p
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y → 0 −∞
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x > 0 x y = ± 1 + x x < 0
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[0, π] utt + 2ut − uxx = 0,
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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,
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∆ = 0 λ = −1 µ1 = µ2 = −
- Page 204 and 205:
x = cos θ y = sin θ F F (co
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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
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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 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