[分析] 小問題

看板Math作者jacky7987 (憶)時間13年前 (2011/09/09 00:38)推噓0(0推 0噓 10→)

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就是在隱函數定理中 Given S is contained in |R^{n+k}. Define f=(f_1,...,f_n):S-->|R^n. Suppose f is C^1(S). Let (x_0;t_0) in S and f(x_0;t_0)=0 and det[D_jf_i(x_0;t_0)]_{n*n} is not zero. Then there exists a k-dimensional open set T_0 containing t_0 and one, and only one ,vector-valued function g:T_0-->|R^n, defined on T_0 satisfying: 1. g is C^1(T_0) 2. g(t_0)=x_0 3. g(g(t);t)=0 for all t in T_0 ==== 我想問的是如果原本的函數是C^2, 會保證g也是C^2嗎? 是的話證明方向大概是(我個人猜測是硬幹XDD) 謝謝大家 ==== 加問一題好了 Find∫ cos(ax+by+cz)dxdydz , where B is unit ball in |R^3 with center 0 B a,b,c are constants -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.251.143.90

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jacky7987

09/09 00:41, , 1^F

09/09 00:41, 1^F

※ 編輯: jacky7987 來自: 111.251.143.90 (09/09 01:44)

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tasukuchiyan

09/09 15:44, , 2^F

09/09 15:44, 2^F

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keroro321

09/09 15:52, , 3^F