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

1 ω(x, y) = M(x, y) dx + N(x, y) dy
M N D R 2
ω(x, y) = 0
F (x, y) λ(x, y)
dF (x, y) = λ(x, y)ω(x, y) λ(x, y) = 0 D
F (x, y) = c c ∈ R S = {(x, y) ∈ D : M(x, y) = N(x, y) = 0}
D \ S
ω(x, y) = 0
ω(x, y) = M(x, y) dx + N(x, y) dy ,
ω F (x, y) dF = ω
∂F
(x, y) = M(x, y),
∂x
∂F
(x, y) = N(x, y).
∂y
F (x, y) ω F (x, y) = c c ∈ R
λ(x, y) ≡ 1
∂M
∂y
∂N
(x, y) = (x, y).
∂x
dF (x, y) = ω(x, y) = 0
ω(x, y) = 0
ω(x, y) = M(x) dx + N(y) dy
f(x) M g(y) N
f(x) + g(y) = c c ∈ R
ω(x, y) =
0
ω(x, y) = ϕ(x)ψ(y) dx + ϕ1(x)ψ1(y) dy
ψ(y) = 0 ϕ1(x) = 0 ψ(y)ϕ1(y)
ω(x, y) = M(x) dx+N(y) dy
M N D α ∈ R k > 0
M(kx, ky) = k α M(x, y), N(kx, ky) = k α N(x, y),