Re: [分析] 隱函數定理
※ 引述《Madroach (∞)》之銘言：
: (1)Show that x^2-y^2-u^3+v^2+4 = 0
: 2xy+y^2-2u^2+3v^4+8 = 0
: can be solve u, v as continuously differentiable functions of
: (x,y) for (x,y) near (2,-1) satisfying u(2,-1)=2, v(2,-1)=1.
: (2)Find the value of du dv
: ----(2,-1) + ----(2,-1)
: dx dx
: 第一小題的部分我會做
: 但是第二小題想不出辦法解出來 Q Q
: 懇請各位強者能指示小弟一點方向
f_1:x^2-y^2-u^3+v^2+4
f_2:2xy+y^2-2u^2+3v^4+8
f_1(2,-1,2,1)=0
f_2(2,-1,2,1)=0
let A=f'(2,-1,2,1)=[ 4,2,-6, 2]
[-2,2,-8,12]
let Ax=[ 4,2] Ay=[-6, 2]
[-2,2] [-8,12]
detAx=/=0
thus existence of C'-mapping u v,defined in a neighborhood of (2,-1)
s.t. u(2,-1)=2 v(2,-1)=1
then -(Ax^-1)Ay= -1/12 [ 4,-10]
[-44,52]
-1/3 + 11/3 = 10/3#
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