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netvisitor

ľ³æ (ÕýʽдÊÖ)

ÒýÓûØÌû:
10Â¥: Originally posted by billiards at 2014-07-05 07:36:09
y=f(x) »òÕß x=f(y) ÆäʵÊÇ¿ÉÒÔÈÎÒâÑ¡µÄ. Ò²¿ÉÒÔд³É a=f(b). ¹Ø¼üÊÇÆäÖеÄÂß¼­¹ØÏµ²ÅÊÇÖØÒªµÄ....

y=f(x) ºÍ x=f(y)µÄ±äÁ¿ÊDz»Í¬µÄ£¡
ÎҵĻý·ÖʽÖÐdxÒÀ¾ÉÊÇdx,²»»á±ädy!
11Â¥2014-07-05 07:40:04
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billiards

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
9Â¥: Originally posted by netvisitor at 2014-07-05 07:34:34
y=x?
f' µÄ±äÁ¿ÄѵÀ»¹ÊÇx£¿inverse functionµÄ±äÁ¿²»±ä£¿
ËäÈ»¸ÐлÄúµÄ»Ø¸´£¬µ«»¹ÊÇÇóÓÐÖÊÁ¿µÄ»Ø¸´£¡
P.S. ÎÒ²»ÖªÄãµÄÒýÓÃΪʲô»á°ÑÎҵġÒdyд³É¡Òdy£¬¡Òdxд³É¡Òdx£¿ÄѵÀľ³æ³öÎÊÌâÁË£¿...

ÎÒ²»ÊÇ˵ÁËÂï, ÏÖÔÚͳһÓÃf(x) ºÍ x À´±íʾ. ¹Ø¼üµÄµØ·½ÊÇÄǸö inv f( ). À¨ºÅÀïдʲôÒѾ­Î޹ؽôÒªÁË.
12Â¥2014-07-05 07:40:31
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billiards

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
9Â¥: Originally posted by netvisitor at 2014-07-05 07:34:34
y=x?
f' µÄ±äÁ¿ÄѵÀ»¹ÊÇx£¿inverse functionµÄ±äÁ¿²»±ä£¿
ËäÈ»¸ÐлÄúµÄ»Ø¸´£¬µ«»¹ÊÇÇóÓÐÖÊÁ¿µÄ»Ø¸´£¡
P.S. ÎÒ²»ÖªÄãµÄÒýÓÃΪʲô»á°ÑÎҵġÒdyд³É¡Òdy£¬¡Òdxд³É¡Òdx£¿ÄѵÀľ³æ³öÎÊÌâÁË£¿...

Сľ³æµÄÒýÓÃÓÐÎÊÌâ, ÎÒ·¢ÏÖÄãÒ²¸ÄÁËÎÒµÄÄÚÈÝ. ²»¹ýÕâÀïÎÒÃDz»±ØÌÖÂÛÕâ¸öÁË.
13Â¥2014-07-05 07:42:14
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netvisitor

ľ³æ (ÕýʽдÊÖ)

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14Â¥2014-07-05 07:49:43
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feixiaolin

ÈÙÓþ°æÖ÷ (ÎÄ̳¾«Ó¢)

ÓÅÐã°æÖ÷

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feixiaolin: »ØÌûÖö¥ 2014-07-06 21:18:37
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f'(x)=sum[an*x^n]
1/f'(x)=sum[bn*x^n]
ÇÒ
sum[an*x^n]*sum[bn*x^n]=1
È·¶¨  b0=1/a0;
          b1=-a1*b0/a0;
         ¡­¡­
Integrate[1/f'(x)]=sum[bn*x^(n+1)/(n+1)]+Const
15Â¥2014-07-05 07:51:28
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peterflyer

ľ³æÖ®Íõ (ÎÄѧ̩¶·)

peterflyer


¡¾´ð°¸¡¿Ó¦Öú»ØÌû

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ÒýÓûØÌû:
5Â¥: Originally posted by billiards at 2014-07-05 07:03:05
Ç°Ãæ·¢µÄÌû×ÓÓÐЩ´íÎó,ÕâÀï×÷¸öÐÞ¸Ä:
ÒòΪ y=f(x), ÇÒ x=inv f(y)
¶øÇÒ (dx/dy) * (dy/dx) = 1,  
ÏÖÔÚ²ÉÓÃÀ­¸ñÀÉÈÕ±ê¼Ç·¨,²¢ÇÒ¶¼Óà f(x) ºÍ x À´±íʾ, ¿ÉµÃ: f'(x) * f' = 1,  ¼´:
        1/f'(x) = f'
µÈ ...

¼ÙÉèf(x)=e^x£¬Ôò inv[f(x)]=Lnx
µ«£º¡Ò{1/f'(x)]} dx =¡Òe^(-x)*dx=e^(-x)+ C
Òò´Ë£º¡Ò{1/f'(x)]} dx ¡Ù inv f(x) + C
16Â¥2014-07-05 08:38:17
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

netvisitor

ľ³æ (ÕýʽдÊÖ)

ÒýÓûØÌû:
16Â¥: Originally posted by peterflyer at 2014-07-05 08:38:17
¼ÙÉèf(x)=e^x£¬Ôò inv=Lnx
µ«£º¡Ò{1/f'(x)]} dx =¡Òe^(-x)*dx=e^(-x)+ C
Òò´Ë£º¡Ò{1/f'(x)]} dx ¡Ù inv f(x) + C...

ËûÊÇû¸ãÇå³þº¯Êý×Ô±äÁ¿µÄ¸ÅÄî¡£
17Â¥2014-07-05 08:52:40
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ÁøÇå

ľ³æ (СÓÐÃûÆø)

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Blow-up
18Â¥2014-07-05 16:10:05
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Nonsmooth

Òø³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
3Â¥: Originally posted by netvisitor at 2014-07-04 19:44:02
µ«ÇóÏê½â¡£ÄÜ·ñд³ö±í´ïʽ£¿²»Ê¤¸Ð¼¤£¡...

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