math一败涂地……

math_sfUID：2155581

那个行列式等于一不见得对吧？！
如果有一个矩阵以1为它的某个特征值，就满足题目的条件阿，但是它的行列式可以不等于1

math_sfUID：2155581

还有，呵呵呵，真是不想回忆，但是看到帖子忍不住阿！
点点收敛和一致收敛似乎不能互推啊~~~~

monochromeUID：2116370

f(n)是n*n*x在0到1/n
       2n-n*n*x在1/n到2/n
其他是0
怎么样呢 好象这样又是点点收敛到0又是积分为1?

[ Last edited by monochrome on 2005-11-14 at 10:31 ]

javahsUID：41473

we also need to discuss the first 30 questions, I remember the second question is to choose a pair points that lies in the boundry of a square that area is one

3: F'(T) = 3F(T) , forget ask for what  , there has 2log3 , 3log2 something in the answer

huangjin_suzhouUID：37183

agree

Originally posted by math_sf at 2005-11-14 00:30
那个行列式等于一不见得对吧？！
如果有一个矩阵以1为它的某个特征值，就满足题目的条件阿，但是它的行列式可以不等于1

[ Last edited by huangjin_suzhou on 2005-11-14 at 05:03 ]

huangjin_suzhouUID：37183

no, only the latter two are correct I think




有一道说f_n均为连续，收敛到f，点点收敛，F_n=integral of f_n，对于0到1闭区间的x。然后有三个命题，答案是都对，因为闭区间连续函数收敛到连续函数为一致收敛，所以三个极限都成立。

huangjin_suzhouUID：37183

no

Originally posted by chrjoy at 2005-11-13 14:07
一致收敛那个我说的对吗？

monochromeUID：2116370

这个就不是一致收敛吧

Originally posted by monochrome at 2005-11-14 01:02
f(n)是n*n*x在0到1/n
       2n-n*n*x在1/n到2/n
其他是0
怎么样呢 好象这样又是点点收敛到0又是积分为1?

huangjin_suzhouUID：37183

consider this function, it converges to one at all rational points r1,r2...rn  in the [0,1],others points 0. fix n large enough
another function 1 at all rational points, other points 0.
the first function is Rieman intergrable, the second not even intergable ( in Rieman sense)

[ Last edited by huangjin_suzhou on 2005-11-14 at 12:17 ]

math_sfUID：2155581

OK , let's talk more about he det.
consider the det((S-I)^2)=det(S^2-2*S+I)=0; so the det(n) may not be exactly n

huangjin_suzhouUID：37183

I didn't catch your point, any step you omited before you draw the conclusion ?
I am in the same boat as you,hehe

Originally posted by math_sf at 2005-11-14 13:12
OK , let's talk more about he det.
consider the det((S-I)^2)=det(S^2-2*S+I)=0; so the det(n) may not be exactly n

〓燃→烧〓UID：2157558

反正我记得比较难的题有 38 51 53 55 。。大家都做得不太好吧。那scale就都高。哈

jitterUID：2158426

i only got det=1, how does anyone get trace=n? i think by applying det to the equation, we can only get a real equation of "det(s)".

about the Riemann mapping problem, f(z)=exp(z) for unit circle, how many component is it? i did not take complex functions class.

taking the test without having breakfast was a real disaster, i felt so aweful finishing up the test. the first 33 problems was ok, and cost about an hour, but i really screwed up.

[ Last edited by jitter on 2005-11-16 at 16:35 ]

icewolfUID：2146015

这里面很多东西有用的说

brahmaUID：2189879

真题回忆，顶