作者winer8 (快來明星3 缺1 )
看板Grad-ProbAsk
標題[理工] [工數]-函數內積和STURM-LIOUVILLE定理
時間Sat Nov 7 22:03:19 2009
2
1.若函數g1=a0 g2=b0+b1x g3=c0+c1x+c2x 在-1<= x<=1之區間內形成單位正交
函數 請求g1 g2 g3
1 0.5 0.5 0.5 2
答案:g1=------- g2=1.5 x g3=(5/8) -(45/8) x
2^0.5
2.define the function
<p(x),g(x)> = S xp(x)g(x)dx (S為積分 範圍從0~1)
is an inner product on vector space P2. Aplly the Gram-Schmidt process to the
2
basis B{1, x, x }on[0,1]to obtain an orthonormal basis
0.5 0.5 2 6 3
答案 u1=2 u2=4(x-2/3) u3=600 (x - ---x + ---- )
5 10
3.find fouriesof f(x)=xsinx
n+1
1 ∞ 2(-1)
f(x)=1 - ---cosx +Σ ------ cosnx 不會算係數
2 n=2 2
n -1
4.define f(t)=t 0<=t<=1 f(t)=0 -1<=t<=0 and g(t)=-α1+α2t where α1
and α2 are costants. determine the values of α1 and α2 so that
2
∫[f(t)-g(t)] dt is minimized ( 範圍從-1~1)
答案 α1 = -1/4 α2=1/2
感謝各位
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※ 編輯: winer8 來自: 114.37.178.201 (11/07 22:04)